The right to vote
Nationals of other european union countries who are permanent residents in France have the right to vote in municipal and european elections, but not national, presidential or departement elections.
You can (should!) register to vote at the Mairie by filling in a simple form with name, address etc.
Download the form here : download form
You will need proof of identity (passport) and proof of residence (recent electricity or fixed-line telephone bill). You will be required to certify that you are a permanent resident and that you renounce the right to vote in your country of origin - this is to ensure that no-one votes twice in european elections for example.
Disenfranchised ? If you feel that it is unjust and undemocratic to be a tax payer in France, but to not have the right to vote in the most important elections - make your voice heard. Complain to your Deputé and your Euro MP.