A significant number of PhD (funded or not) and internships are listed on doctoral schools web pages. See, e.g., https://www.edpif.org/fr/recrutement/prop.php

If a PhD is advertized, and appears as “not funded”, the meaning is that a fellowship can be obtained during the yearly competition that often takes place between April and June. Be aware that the corresponding applications often have to be submitted rather early (April ; cf. EDPIF web site, or other doctoral school websites).

An internship in France or abroad cannot start without a properly signed internship agreement (“convention de stage”). The documents to be filled are here. Start this paper work as early as possible.

Internships (€€€ = with funded PhD)

Funded PhD