Originally Posted by Bevdeforges

As the spouse of an EU national, yes, she should have the right to work and to travel within the Schengen region on her carte de séjour.

Thanks for posting that paper from your prefecture. I note they ask for a birth certificate with mention of the marriage. It's sometimes necessary to explain to the folks at the prefecture that other countries don't always update birth documents for events like marriage, divorce and death.

Your marriage certificate ought to suffice, though if your spouse has been married before, they may want either a divorce certificate or a death certificate for the ex-spouse. You can normally argue them out of this (nicely - just explain the difference in documentation) - but it's safest not to mention any prior marriages in the first place if they aren't relevant to the event at hand.
Cheers,
Bev