According to this article, Royal miscalculated the gender issue. Instead of focusing on specific programs and ideas, more voters felt she used her gender as bait. Knowing that I lack a deep in-depth knowledge of the French electorate, I cannot say much more than that. But to bring this home, I would caution the American electorate against using the gender issue as the sole reasoning for supporting Hillary. I think it's shallow and if the French election is any kind of indication, it's not particularly a successful strategy.
French Ex-patriot voters.
Link to numbers. (HT: SuperFrenchie)
This was pretty fairly predictable. Many (but not all) have left France for more economic and business freedom and Sarko was their man, pretty much from the beginning. It wasn't an extremely wide margin, but if Royal were to have won this particular vote, I think she would have won. (I don't base this on numbers, just political intuition.)
Some post-election statistics.
Arrests for rioting 592
Vehicles burned 730
Police officers injured 28
For complete analysis from someone more in the know than me, give a look at Amerloque's post-election analysis. In the time I have come to know him in the blogosphere, he has proven time and again, he is a good and trusted source of information.
Read The Right Revolution For France by Dominique Moisi,
Sarkozy's Dangerous Strengths by Jim Hoagland,
Sarkozy Must Ring The Changes by Anthony Daniels,
and this editorial from the Telegraph for more perspective.