As of October 2012, GMail includes its own multilingual options which may help here.
If you tick "Enable input tools" under "Language" in Settings, you will be prompted to choose from a long list of languages and foreign keyboards. In your case, choose the French option with a keyboard symbol next to it.
Once this option is enabled, you'll see an extra icon next to the Settings cog in the top-right. In your case, this will have a picture of a keyboard on it, as you'll have chosen a virtual keyboard earlier.
When you click it, a virtual keyboard will be displayed from which you can enter foreign characters. Note that you'll need to have focus on the message box you'd normally type in before pressing keys on the virtual keyboard.
One catch - in my experience, turning on a foreign virtual keyboard also causes GMail to map your real keyboard to the foreign key-map. So QWERTY becomes AZERTY for France etc! Therefore, you'll probably want to turn off the virtual keyboard when you're not entering special characters! Thankfully this is a one-click operation - just click the X in the top-right of the virtual keyboard.
(Most of this information originally from http://uk.queryclick.com/seo-news/gmail-goes-multilingual/)