Residence permit holders in the Schengen area (certainly in France) typically don't have or need a visa to enter either their country of residence or the Schengen area as a whole.
You simply present the residence permit (together with your passport) to the border guards or, if needed, to the airline when boarding your flight. In the first few years of this system, some friends did come across airline/ground handling personnel who were unfamiliar with these residence permits but they should at least be able to call a supervisor or to find documentation confirming the rule. I would hope most are familiar with them by now.
A Schengen residence permit can also be used to travel to Romania, Bulgaria, Croatia, or Cyprus without a visa (but you still need a travel document). You will find documentation to that effect in many places, including for example on the website of the Romanian Ministry of Foreign Affairs:
V. Do I need a visa?
[…]
- NO
[…]
The holders of Schengen visas with two or multiple entries, national visas or residence permits issued by Schengen Member States.
As you can see, the exact same rules apply to residence permits and to valid Schengen visas.
Note there are different types of carte de séjour but all of them should count as a residence permit under the Schengen regulations (in French “titre de séjour” and not “carte de résident”, which is something much more specific). A “récépissé de première demande de carte de séjour, “autorisation provisoire de séjour” or “récépissé de demande d'asile” however does not. See vosdroits.service-public.fr.
