Diversity: some of the more noteable resistance groups

(A German poster showing the members of a communist resistance movement who have been executed)
The number and diversity of Freedom fighters was immense. Soldiers and citizens from all walks of life organized their own gangs, which in turn would work together on a particular task. Most of these parties were loyal to a particular political ideal, region, or religion, though most were openly loyal or at least worked in collaboration with the Free French Forces.
The largest and most organized group of fighters were the Free French Forces (.F. Ellis, Allen, Warhurst.Victory in the West p. 573-584). These soldiers represented the French Provisional Government and were often the most well informed as well as the most well trained (because many were former soldiers) (Sumner, The French Army, pp. 29-30)
The majority of French Resistance fighters outside the control of the Free French were from radical political groups. These groups, usually nationalist or communist, would work to an extent with the French Provisional Government (though the communists more often took orders from the USSR) but for the most part attempted to stay independent. (Jackson, France: The Dark Years, pp.114-115)
The communists in particular would not engage in active resistance until the invasion of the USSR, at which time they began to actively organize. The communists ended up being the most successful of the groups outside control of the FPG. By 1941 they had committed several high profile assassinations and sabotages. (Jackson, France: The Dark Years, p. 121) Many of these Communists had fought during the Spanish Civil war, and as a result, were hardened and well practiced to guerilla warfare.
Another group that had an exceptionally high percentage of its members join were the Jews. Despite only representing a tiny fraction of the French population, Jews made up nearly a quarter of Resistance members.(Suhl, They Fought Back, pp. 181-3) These Jewish Fighters had a reason to join in such numbers. The Vichy Government had passed laws that removed citizenship from Jews making it possible for Nazis to arrest them. Therefore, many Jews went into hiding; or worked for the resistance.
The BCRA network was a division of the Free French Army that focused almost entirely on espionage and information gathering. Organized out of former members of the French Intelligence Agency, they provided the allies with maps and photographs of German positions, weapons, and fortifications. The BCRA also participated, to a lesser extent, in assassination plots.
Lastly, a population of Spanish communists, and German, Italian, and to a lesser extent Austrian, anti-fascists moved to France to join or aid the resistance. The Spanish tended to join private groups, as they were working ultimately towards the downfall of Spanish fascists leader Franco. However, the Germans, Austrians and Italians worked directly along with the FPG to commit acts of sabotage, espionage and assassination.