I am a Malaysian with Bewilligung C, married to an Englishman in Zürich since 2015. In three weeks I will be starting a new job in Geneva.
As I will be working 50% there, friends have suggested I can find more reasonably priced accommodation across the border in France. It would only be 2-3 days a week, circa 11 a month.
Wait a min. We may not be understanding well your situation.
I assume you have a C permit from Zurich canton and you will keep your main residence in ZH. But, you'll start a part time job in Geneva. Thus, you need a place to sleep a night or 2 during the week in Geneva, or near Geneva.
If the above assumption is correct, by renting in France you're asking about a Wochenaufenthalt (week stay) in France. No idea if this is possible, I've only declared a secondary residence or Wochenaufenthalt in another canton before.
But, if it's only a few days per month, you may stay in a hotel in France and go to your job in Geneva. This may be even cheaper than paying for a "lower cost" rental in France. For this, you don't need an additional pemit and it may even be tax deductible.
Except, that even with a C-permit, a non-EU citizen is only allowed to be in the rest of Schengen for 90/180 days. So the OP would be eating into their travel allowance by staying in France every week.
True. 11*12=132 < 180 days. So, there would be ~50 days left to roam around the world and still meet the permit C requirements. If traveling is important, this is a limit.
Otherwise, find an apartment in Geneva, declare it as secondary residence (wochenanfenhalt, résidence secondaire) and deduct from income for taxation purposes.
If I'm right CERN employees don't pay taxes at all, but then they don't have any Swiss retirements contributions nor permit/citizenship entitlements. Maybe that's different if you've already have Swiss ID or permit.
Hey, don't forget that housing costs as Wochenaufenthalter are tax deductible. So, maybe it's not necessary to find a lower cost place to rent in first place.