Currently at Capgemini and client want me to hire full time with them, do Capgemini make any problems client hires.

They usually don’t accept that unless they do some kinda negotiation. Like sell you or add another resource.

If you are in California you don’t have to worry about this. I have seen many switching to full time roles with the client in the past and never heard any issues by CG.

Depends on the agreement signed between CG and client

It depends on the country and the state/territory that you’re in as well as the relationship between Capgemini and the client and the relationship between Capgemini and you.