Hi Edouard ,
So basically, you need your vServer to accept requests on both TLS1.0 as well as TLS1.2 if I understood it correctly.
If that's so, then you can keep TLS1.0 as well as TLS1.2 enabled under associated client ssl profile. So single client-ssl profile will accept both requests and it will negotiate client on best possible match.
Additionally, if it is possible, try to keep all your vServers running on min TLS1.2 as lower SSL/TLS versions are prone to different vulnerabilties. You may be already knowing this but just thought of highlighting this also. Ty!
Hope it helps!
Mayur