No that's not really the truth. The Algerian gangs are the most high profile because they feud with each other and most of the killings happen in the Algerian neighborhoods. They mostly dominate the retail drug trade. They definitely move a ton of drugs, but they tend to stick to the retail side of the trade.

The ports are still under the influence of the Corsicans, so nothing comes in without them knowing about it. Illegal gambling, skimming casinos and slot machines...rackets like that...are dominated by the Corsicans.

The situation in Nice is kinda the same as in Marseille.

In Paris the retail drug trade is also dominated by North African gangs. A lot of Algerian crime families, but in Seine Saint Denis for instance there are also quite a few Tunisian crime families active. Again they tend to stick to the drug trade. It's the same in Grenoble, where there are also quite a few Tunisian crime families active (especially in the Villeneuve area).

The more "traditional" French underworld still has a presence in Paris as well. The most infamous are the "gypsy" families, most of them of Yéniche backgrounds (the Yéniche are an indigenous white European group of travellers originally from Switzerland, but many of them settled in France). They're local outfits centered around those families, but those groups are very mixed with French, Yéniche (most Yéniche that grew up in France regard themselves as "French" and quite a few are even very patriotic) and also criminals of North African and Italian descent operating in the same group.
They're active in quite a few domains; professional robberies, extortion, importing drugs...they also own quite a bit of property in their respective areas...

The traditional French underworld also has a presence in other parts of France: the Vaucluse (with its main city Avignon), the Nord Pas de Calais region...but also Marseille (mostly in the Etang de Berre area)...