Hello. You might want to purchase the book, "Going Local, Your Guide to Swiss Schooling," by Margaret Oertig. Here's the link:
http://www.bergli.ch/100/con_liste.asp?prono=72 It has a massive amount of information, much of which you won't need for your one year, but it also has a lot of reports on expats' experiences with state schools in Switzerland that would help you prepare to get the most for your kids during your year, and perhaps avoid some pitfalls. It really supports, or even advocates, entering your kids in state schools here when feasible for a family's circumstances, without in any way judging those families who choose international schools (and, indeed, noting the different advantages of the international route).
I truly understand and respect your desire for your children to really learn French (I hope you have them in classes now because every bit of French they can learn beforehand will really, really help them get a good start here) and really experience local living while you are here. And I can tell that you don't want to hear anything more about private schools, so I will bite my tongue! And, again, I really respect your determination. But consider one other factor that could affect your kids' experience here and whether they get out of it what you are hoping. Switzerland culturally is NOT France. For a lighthearted, easy-read, tongue-in-cheek look at the Swiss culture, you might read the the Xenophobe's Guide to Switzerland (and the Xenophobe's Guide to France for comparison). It will be really important for you to come to Switzerland prepared for the culture since you won't have the luxury of learning by trial and error over time.
The Going Local book has some blurbs from English-speaking kids who have started in Swiss state primary school. Some found it difficult to break in socially because, apparently, in many cases friendships form in enfantine/kindergarten/1H-2H, and classes tend to stay together and form fairly tight-knit groups. My kids aren't old enough for me to know from first-hand experience, but social reserve and slowly-developed, long-term friendship is certainly a recurring theme in observations about the Swiss. If your kids can't make friends, they may not learn French very well (a lot of language learning happens, of course, when they make friends), or enjoy the experience at all. Maybe you would still have been glad of your experience in France even if you had been unable to make friends....or maybe that would have altered your entire outlook toward French and language-learning.
Anyway, just keep in mind these challenges that you will need to overcome for your kids to make friends and learn French and have fun:
1. the state schools in Fribourg are big, and some of the schools are considered rough (by the Swiss, tho, I am not at all sure that an American would see them as rough) and can be intimidating (Vignettaz less so). Can you make a visit to check out the area and see the schools?
2. there are no school sports-teams (or chess clubs or whatever) or any after-school culture of the kind that you may be used to in America (though you can sign your kids up for one extra-curricular activity each, which may or may not take place at your school)
3. parents do not take their children to and from school when they are as old as your children (by then Swiss children are pretty independent, and all who attend Fribourg state schools live within walking distance) so your ability to connect with other parents and arrange "play dates" for them will be really limited
4. another poster to this thread is correct that in Fribourg your kids would be two of many foreigners (no particular excitement about it). And the poster from Bern is correct that there are few native English-speakers in the mainstream classes in Fribourg, but I don't know how the schools handle primary-school kids who don't speak French--apparently in many areas they mostly attend welcome classes at first, which would mean your kids would become friendly initially with other non-French-speaking kids, and perhaps some of those might be English-speaking, which could derail your plans. Mainstream class kids the age of your older son will have had a year of English in school, and this might help your son socially because English is a little bit "cool" here, so kids may try to speak it with your son, which is at least some kind of foot in the social door for him, but they won't speak it well enough for English to be the default language, as long as your sons can learn some French before they arrive.
5. the Swiss kids in the mainstream programs may not be especially welcoming (not because they are unfriendly, just that they have their groups of friends already, and Swiss kids are not French (or American) in terms of wanting to talk to anyone and everyone and being open to making a new "best friend" every day, making and shedding friends fairly casually. I don't find the Swiss cold or unfriendly at all--quite the opposite--but I am someone who doesn't need a lot of social engagements, and I'm not sure that Swiss kids make the same effort that many Swiss adults do. And it has been easier for me than it will be for you because I have young kids, so it is easy to talk to other parents on the playground, not like in primary school. And we're here indefinitely. I do kind of agree with another poster that on some level the administrative support you receive at the state school may subconsciously be effected by your short stay. Lots of immigrants really need to learn French for their ability to function in the long term in Switzerland, and the school needs those kids to learn because the school is responsible for them for the coming years. And I think the Swiss kids, and possibly parents, might discount you a bit also, knowing you'll disappear off the face of the earth in a year.
But I think with the effort you're obviously willing to put into it, you can have a great experience, and achieve your goals for your kids! Perhaps you can really focus on structuring all your decisions around promoting language-learning and therefore on forced interaction. It's not France, people don't hang around conversing in cafes just for the heck of it! You'll need to seek out situations that involve purposeful engagement. Find groups. Scouting would be perfect, but here in Fribourg I think it only exists in Swiss-German. There are lots of athletic "clubs" because of no school sports teams, and you can find music lessons at the conservatoire. You can find activities and sign your kids up from the U.S.--and you should because things fill up. (Speaking of which, um, housing? I kind of thought you had to arrange that farther in advance than just a few months ahead. Do you have leads on areas that you are considering?)
Even if you are against "overprogramming" your kids in the U.S., you should abandon that for this year. I could see someone thinking it would be best to leave the kids' schedules open after school so that they are free to make friends on their own, but that would be a mistake here, given your goals. Group activities where the kids all speak French but the teacher is also able to speak English might be great. It will be easier for your kids to learn French if the teacher can put in a key word or two, I think, and it doesn't involve a risk that your kids will be able to lapse into conversing in English. You are obviously well aware that you have to avoid native-English-speaking kids and groups like the plague!
And, ok, I can't help it, I have to suggest that you think just once more about private school. Not international school, not English-language school. A school I've written about in Fribourg is ELPF, a small, Swiss, French-speaking private school. Consider living in Fribourg if you will work in Lausanne or Bern
Just to show you how not-international it is, I'll tell you that the tuition this year for one child was 5,800 CHF (but likely will increase some as it grows) vs maybe 30,000 CHF or so for an international school. (There aren't any in Fribourg, but I've heard they are at least 30,000 elsewhere.) Tuition for additional children is discounted, so for your two kids you'd have paid just 9,600 CHF (total for both tuitions) this year. If you want your kids to stay at school for lunch (or to go early or to stay late), that costs more, and the cost depends on how many days you want that extra time. There is no instruction during this time, just kid-to-kid interaction, so plenty of time to socialize in French!
The advantage to you would be that it is a small school and easier for you to meet other parents (in order to facilitate socializing for your kids) and for your kids to make friends (it's got a small-community feel to it, and is small enough that I imagine the primary-school kids actually do welcome newcomers). It doesn't have the resources for regular and mainstream classes, so it would be total immersion for your two from day 1! (Assuming the school was willing to take on non-French-speakers--it has a reputation for being somewhat more rigorous academically than the state schools and wouldn't want to slow the other kids down.) I imagine you'd need to get a tutor for the kids--perhaps you could find a university student willing to sit in on your kids' classes and help them at the beginning? Anyway, I'm done and hope I haven't offended you. I really, really support your enthusiasm and determination for language learning, and I think state schools in the Fribourg area could be a great way to go, as could the private school in Fribourg.
Wait! One more thing, whichever school you go with, maybe post a question to the group about what kinds of things 9 and 11 year old boys think are cool that are not readily available here in Switzerland and that you could pack in your suitcases? (I have young girls and no clue for the older kids.) Little things that could facilitate interaction or serve as token gifts if/when they get invited to another kid's house. Or things to exchange, like whatever the current hand-held game system is for the age group, you might check out whether there are compatible cartridges/games here and bring extra cartridges so that your kids could loan/trade their English ones for for their classmates' French ones. (English is a little "cool," as I said above, and parents here do want their kids to learn English, so, frankly, your kids might be more welcome in their homes if they can also help their friends learn English or at least want to learn English.)
And maybe post a question asking if anyone here has contacted a teacher before arrival to ask if there is anything they could bring for their kids' classes to enjoy on the first day? Or if their class will perhaps be studying anything during the course of the year that you could "accessorize" from America, like bring packets of NASA freeze-dried astronaut ice cream if they'll be doing a unit on space (many people here have never heard of it and few always wanted to try it), or bring some vintage gee-gaws you can get off of eBay for whatever historical period they may study. (Ebay doesn't exist here.) For end-of-school or Xmas gifts to teachers, we've done things like gift boxes of Jelly-Bellies, maple-syrup samplers, things like that, and the teachers have loved them because it gives them a taste of something genuinely American/foreign that is not available here. (It is REALLY hard to think of American things to give for gifts that wouldn't seem offensive or condescending or poor quality/unnatural and that aren't already available worldwide.) But, ask the group maybe before asking a teacher--teachers tend not to disclose as much about lesson plans in advance as American teachers do, and I don't know if it is on principle or not, if you might be seen as pushy or intrusive for asking. I'm still really new here.
Good luck!