As written, the limit in France for legally riding a bicycle is 0.5 gram of alcohol per liter of blood or 0.25 milligram of alcohol per liter of air exhaled.
And the limits are strictly enforced. By that I mean that if you're caught riding over the limit, expect repercussions. I believe it's currently a 135€ fine.
But (and it's a big but) traffic enforcement in France is much, much, much less prevalent than in the U.S. You can drive for years in France without encountering a case of someone having been pulled over by police or gendarmes.
The reason is that French law enforcement relies on automatic measures to catch infractions such as speeding, tailgating, and red light running. French police devote much less time (almost none) to active traffic enforcement, unlike American police, who tend to use traffic enforcement as a fundraiser for local governmental coffers, or as a fishing expedition to find people to whom the police want to demand "compliance.".
That said, there are checkpoints in France. I've encountered precisely two in over a decade of living and driving here: one related to Covid travel restrictions, and one related to catching celebrants who may have done too much celebrating at D-Day commemoration events in Normandie.
So yes, you could get "pulled over" for riding a bike while over the limit. It could happen. But unless you're out on a public road making an obvious nuisance of yourself and endangering either yourself or others, the probability of that occurring is vanishingly small.
Drink responsibly. Bike responsibly. But be realistic.