You can renew your EASA medical anywhere in Europe, but if you want to have a Swedish licence then you will need to start the SOLI process, in which the French authorities will send to the Swedish authorities your medical files and you will be issued a Swedish medical. You can do this at any time. The process takes, on average, 2-3 weeks, but it depends on the authorities involved. I would expect the French and Swedish authorities to be somewhat more efficient than the Italian, Polish or Greek ones...
And why would a French CPL limit your job opportunities?
Holding two medical certificates is not allowed. At least theoretically... Don't know what would happen in case you get caught. You're fit to fly, maybe just a fine.