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.

This “nobody cycles in bad weather” is a tired myth. Yes, there’s some truth in it but cycling numbers past the traffic counters in my city in the UK (very similar climate) dip by 10-30% in winter months, and the higher end of those is mostly leisure routes not commuting ones. The Netherlands has a lot of rain and much more cycling than most other places.

This is overblown. I visited Tokyo recently and a friend of mine was constantly riding his bike around in the middle of a cold and snowy winter. He wasn't the only one, either.

> Paris can be cold and rainy

I cycle in Paris every week, and the only annoying experience climate-wise is the extreme heat you can get some days in july and august. If it's cold or wet, you can just wear appropriate clothes and be comfortable. But if it's sunny and 35°C, you are going to be drenched in sweat no matter what! Of course, being in the metro those days is even worse...

Put on a jacket.

One of the saddest effects of car-dependency is people forgetting how to dress themselves for the weather.

I have cycled every working day in The Netherlands and in Germany for years (in Germany it was 22km per day) and I would often cycle a bit recreationally in the weekends. It really isn't an issue at all. I just have a waterproof jacket (one of those that circulate air as well), water resistant shoes, and rain pants. On very rainy days, I would put on the rain pants and would arrive mostly dry.

It is not really an issue.

The only thing that was slightly meh was the yearly ~two weeks of thick snow in Southern Germany. It increases effort a bit, but still not a huge issue and the cycling roads got cleared pretty quickly.