As I've gotten through more and more of the coverage about the manif for all, I have realized that a major demand of the protesters is that Hollande delay the January 29 vote on same-sex marriage, in favor of a popular referendum. This is similar to how the debate has played out in the US, too.
According to the article published on BFM TV here, 69% of French respondents in polls agree with the protesters, to the extent that they'd rather vote on it instead of see the French parliament impose the change on the 1793 Code Civil from above. Translation here, between bold lines of original French. This piece came out on January 3, 2013, without an author.
Homosexual marriage: A majority of French people want a referendum