Le Figaro has a detailed set of election returns from last Sunday's vote, with percentages broken down by department (roughly, county) and for Paris, arrondissement (roughly, neighbourhood). I don't have the technology to do a cool red/blue map, so I made a little list (below).
No big surprises. In general the wealthier arrondissements to the west support Sarkozy, the immigrant and less expensive areas to the east support Royal. The urban middle is a pretty even mix. As an American I mostly understand "Sarkozy: conservative, Royal: liberal" but in fact it's much more subtle and complex than that. Any by US standards, they're all flaming liberals.
Sarkozy Royal Sarkozy Royal 1eme 39 28 11eme 26 41 2eme 31 35 12eme 32 32 3eme 29 37 13eme 27 37 4eme 34 32 14eme 30 34 5eme 33 32 15eme 41 24 6eme 44 24 16eme 64 11 7eme 56 15 17eme 46 23 8eme 58 14 18eme 23 42 9eme 35 32 19eme 28 40 10eme 25 42 20eme 23 42 Total 35 32
I left out Bayrou and Le Pen, the 3rd and 4th runners. Bayrou outpolled Royal in the 7th, 8th, and 16th! If facism is your thing, the 18th had the most votes for Le Pen at 5.2%. It also had some of the fewest for Sarkozy; go figure.
Update: thakns to JY I found a map of election results. Charmingly coloured pink/blue!