Yes, it's called "cavalier législatif" ("law rider"?) and it's kind of forbidden by the 45th article of the current constitution, which states that an amendment

Yes, it's called "cavalier législatif" ("law rider"?) and it's kind of forbidden by the 45th article of the current constitution, which states that an amendment is examined if it has a "link, even indirectly, with the piece of legislation being voted". That doesn't prevent it from happening all the time, of course. The Conseil Constitutionnel sometimes strikes the "riders" if the law being voted is referred to the Council -- but referral isn't mandatory. https://www.conseil-constitutionnel.fr/publications/titre-vii/le-controle-des-cavaliers-legislatifs-entre-continuite-et-innovations https://www.conseil-constitutionnel.fr/publications/titre-vi... [in French]