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Given they can request your details from a car hire company for parking fines, I don't see this as much different. I can't be bothered finding the wording of the regulations but it's also possible it's a criminal offence rather than a civil one. Question is whether Strava would refuse to do it given they're based in the US.
Chances are more one of the following:
1, Someone trolling a mate
2, French police posting in the hope it generates paranoia in people and they stopThere's a load of accts purporting to being Police Nationale on Strava though so all/none of this could be real :)
Data access request from the police to get credit card details for premium members of Strava? Probably would cost more than 135 euros in police time though