Go on then, I'll pitch in and help since I'm on the same time zone.
Which canton - the education systems differ, as they're not federal. That said, Harmos is supposed to pulling them closer together. As you've surmised, Harmos is an ongoing project to take the mishmash of cantonal education systems, with their different content, age at which they start, cut-off birthday date at which they start, age at which they stream, do they do one or two secondary streams, etc etc etc, and to align them so that people moving 20 miles up the road don't find that their child is utterly at sea in the new school, in a completely different grade and having no idea how to conjugate the conditional or multiply fractions when the rest of the class did that two grades ago.
At almost 5, she'll go into the first year of enfantine (KG), which may or may not be compulsory depending on your canton. She will probably do 4 mornings and 1-2 afternoons a week, with Wednesdays completely off and home for lunch for at least 2 hours each day.
I'm not sure there IS a French-speaking International school in the French-speaking part of Switzerland..? If you want her to learn the language, the local school will be just fine, or private school if you prefer, perhaps for the increased hours or wraparound childcare. Be aware that the local view of private schools in Switzerland is that they're for children who aren't coping academically or socially in the local system, although of course there may be valid childcare reasons for choosing one.
As for the rest of it... she's 4. Chill. There's REALLY no point fretting about what she'll do in over a decade's time, as you don't seem sure where you'll be living then!
If it helps, I've just moved my English kids from 3.5 years in the local Swiss system to the US, at ages 8 and 12. They are just fine; my 12 year old's just finished 6th grade with As and Bs despite not having written a word in English since he was 8, and my 8 yr old is making rapid strides in reading and writing in English despite being barely unable to sound out c-a-t when we arrived 6 months ago (she was about a year behind the others then but is now perhaps 3 months behind according to her teacher, a difference that'll vanish by Christmas).
I know that the US is all about the grades and the transcripts, but it was really no bother turning up with my kids with no academic records and no education in English for the last few years. The school just shrugged, put them in their chronological year groups, and figured it out from there; I think my daughter's been getting a bit of extra one-on-one reading support, but otherwise they've just slotted in.
The only gap bridging I did was to try and teach my daughter the basics of reading in English, and making sure my son knew about things he hadn't even started in Math in Switzerland but were key in the US, like fractions.
If you stay in Switzerland, you'll have no problems at all. A 4 yr old will be utterly fluent long before she needs to be streamed for secondary education, so she'll either be bright enough to be considered for the university stream, or she won't; you can worry about and research extra support if necessary once she's around 9 or 10.
She won't be streamed based just on exam results, by the way. Again, it's canton specific, but the norm is some combination of her GPA in key subjects like French, German and Math, along with her overall classroom behaviours in things like independent working, self-discipline, etc. If you want, though, you'll probably find examples of the cantonal test past papers online; Vaud definitely has these. That'll show you the sort of expected level.