No, it's worse than that. The French spying apparatus has way less legal boundaries because the government basically doesn't want to acknowledge the spying even happens.
At least you can argue in an American court that you have standing if you have proof the NSA is spying on you
... and? "Way less legal boundaries" — the NSA doesn't even have a published budget. If you're on the internet, you're in their database(s) and so is your data. If you're interesting to them, your sysadmins are already exploited.
Court? Legal avenues? Legal boundaries?! Surely you jest.
and do you think the DGSE is some sort of transparent body?
They're obviously both groups you don't want to have as buddies, but the NSA has lost court battles before, and ends up complying with the rulings most of the time.
The French surveillance services openly gloat about working in a "judicial vacuum": basically all the rules of its operations are decided by the Prime Minister and their pals, and basically have no legislative boundaries.