No Service Public page mentions business cards as such. Service Public does, however, require identification details on advertising material, printed matter included, and on commercial documents in general. A card handed out to promote your business comes close, so our advice is to add these details in small print, in French, as French clients expect them.
Company (SARL, SAS, SA): SIREN number; RCS followed by the registry town for a trading business, or RNE for a craft, liberal or farming activity; registered office; share capital for a SARL or SAS. Sole trader and micro-entrepreneur: the same identifiers and, since 15 May 2022, EI or entrepreneur individuel before or after the name; Service Public mentions a fine of up to €750 if it is missing.
Regulated professions such as lawyers, nurses and estate agents have their own communication rules set by their professional body; check them before printing. On the back, add a vCard QR code that saves your contact in one scan, and to choose between a chip and a code, read our NFC business card or QR code comparison.