French citizens and headquartered corporations cannot answer a foreign justice request concerning some things (pretty much everything as the wording is vague) without refering it first to the french government. Failing to do so exposes to fines and possibily jail.
"Loi n° 68-678 du 26 juillet 1968 relative à la communication de documents et renseignements d'ordre économique, commercial, industriel, financier ou technique à des personnes physiques ou morales étrangères"
The law mentions that it is forbidden to do so "sous réserve" (not sure how to translate that, "without prejudice" ?) of international treaties. I'd be surprised if there were no such treaty between France and the UK, or if it wasn't part of the EU treaty.
https://www.legifrance.gouv.fr/loda/id/JORFTEXT000000501326/...
"Loi n° 68-678 du 26 juillet 1968 relative à la communication de documents et renseignements d'ordre économique, commercial, industriel, financier ou technique à des personnes physiques ou morales étrangères"