You can basically choose as long as you have a valid passport of a non-European state (which is not the same as the EU btw) you can go for Eurail, or you go for Interrail as a French resident. The only difference is that there’s a limitation on the travel days in your home country for Interrailers (max. two days for most countries).

See link below:

https://www.eurail.com/en/help/interested-in-eurailing/do-i-need-a-eurail-or-an-interrail-pass