The French exercise passionately but never frantically. Blend in with the local fitness culture.
Every arrondissement has a municipal pool open to all for €3–5 per session. Join a club (association sportive) for monthly access under €30. Far cheaper than private gyms.
Vélib' (Paris) and similar bike-share schemes are €3/month with a student card. Cycling is the fastest way across most French cities — and the most French.
The French sports system is association-based. Join a local tennis, football, or running club ("association loi 1901") — rates are subsidised and it's instant social integration.