There is a de facto ban since all donations above EUR 150 must include the donor's identity.
"Moreover, the law does not require the identity of donors to be disclosed, and the possibility of making cash donations of €150 or less entails risks of anonymous donations and leaves the door potentially open to donations from legal persons"
Source: GRECO (2009) Third Evaluation Round. Evaluation Report on France, Transparency of Party Funding. Strasbourg, GRECO