Earlier quoted context omitted.
Armies need resources; people are resources. So the argument isn't, "X is what the enemy wants," it's, "X allows the enemy to recruit more troops." Thinking like chess -- you'd probably avoid moves that gave the opponent more pieces. Especially when those piece spawn by your king.
I was speaking abstractly, not about the OP theme - a logical fallacy is a logical fallacy, even if it provides a useful heuristic. Even if the opponent wants you to do something, it might be the best for you. Think about the game of chicken [1] in game theory. If the opponent puts on a blindfold and makes a precommitment, they want you to swerve - that's what they want! But it would be foolish not to swerve and cras…
It's only a logical fallacy because you've decided to ignore the predicate statement ("this was a strategy for recruitment") and focus on the implication of it ("extremist groups supposedly want exactly this to happen").
The crux of the OP's argument is that aiding in the recruitment of ISIS is not in the best interest of the French, yet that's what this policy is doing.