Join an association
Associative life has a key position in France: 16 million volunteers, almost 2 million employees. They bring to life 1.3 million active associations which play a role in all areas of the social, cultural and economic life of the country: charity, health, education, sport, culture, social life…
Everyone can take part in an association or create one, whether you are French or not.
Many search engines can help you find volunteering missions close to where you live. You can for example go to tousbenevoles.org. You can also get more information at the mairie (city hall) of your city.
If you are thinking to create an association, you can find out more on the procedures on smartexpat.com. You can also get help and resources at the Maisons des Associations (go to maisonsdesassociations.fr, website in French only).