It’s a little tricky and I’m not exactly sure how the French pass works.  While there are some single country passes that are “eurail passes” that is not the case with the French pass.  With eurail passes, you get one pass which lists both names.  While either of you can use it alone, the other has no pass to use.  With Britrail passes, you get separate passes — one of which will say “valid only with ….” and shows the name listed on the other pass.  With the Britrail pass, I could travel without my husband, but he couldn’t travel without me.

The bigger issue is validating it.  Technically you have to both be present and show your passports to have your pass validated before you can use it. This pasted from ricksteves.com:

I had to round us all up to get the pass validated on one occasion.  On another, the ticket agent (at the TGV station at CDG) validated it after checking just my passport.  I’m not sure whether that was standard procedure, oversight, or the result of the fact that the only other person in view was my elderly mother and obviously my traveling companion.

In any case, make sure your husband’s name is listed first when you buy the railpass.