You can drive with your EU license until it expires (and therefore needs to be renewed) or until you commit a driving offense, in particular one that would result, under French law, in the cancellation or suspension of your license (at which point you might have to get a French license only to surrender it).
Until recently, France issued driving licenses with no “administrative validity” period so that similar licenses from elsewhere in the EU could be used indefinitely and did not need to be exchanged at all. Since 2013, France issues licenses with a limited duration (in application of directive 2006/126/EC) but current licenses will remain valid until 2033 so I assume that other EU licenses will also remain valid in France for the same time. After that, everybody in the EU should have a license in the new format and if you have an old lifelong license from another country, you will need to exchange it in your country of residence.
Official source is, as always, service-public.fr and specifically “La demande d'échange est facultative. Ce n'est pas une obligation, sauf en cas d'infraction routière […]”
The documents needed are mostly the license itself (and sometimes, annoyingly, a translation), ID, photos and proof of where you live (in France, typically this would be a utility bill).