Appraising Craft CMS - newbie questions
Craft is the perfect CMS to handle everything you just pointed out.

Can Craft CMS handle bilingual sites? YES.

https://craftcms.com/docs/localization-guide



Is the Craft CMS admin available in French? YES.

https://craftcms.com/support/cp-languages



Can my client set up different user permission levels?** "YES".

Depending on your use case this will be doable. Then its just a matter of "how" your client wants to be able to do this. Craft supports dynamic user permissions creation so whatever your use case is I'm sure Craft will handle it with ease.