I live in the Netherlands where the weather is arguably tougher than in Paris (rain, cold and wind for large portion of the year) yet everyone bikes year in year out.
And not just young active people, it's a habit found across all age groups, parents bike their children to school (or with them if old enough, etc.)
All that to say I wouldn't worry too much about the feasibility issue, it's really more of a mindset to adopt, and it's happening more and more in France.
In amsterdam, few people wear modern/synthetic rain coats as well. Just riding around in the rain with what I assume must be waxed duck out something
> the Netherlands
It's completely flat and the obvious reason why everyone cycles. Nothing to do with mindset, like you're somehow superior to the rest of EU.
Paris has one thing that Amsterdam does not that makes cycling more challenging: elevation. (Ok, Amsterdam has bridges but those are for the most part really short and momentum is enough to carry you across).