how did the detective know the french guy killed his cousin?

It's been a while, but did it have to do with ballistics? Wasn't the gun found in the room the same gun that was used to kill his cousin? I don't remember for sure.

I think a lot of it was circumstantial.

They found a couple in the room, a known violent criminal, and the security guy, and they, incorrectly, connected the dots: the violent criminal was attacking the couple, the security guy tries to save the day, they all die in the cross-fire.

And I think the cop doesn't suspect that Charles was involved in the events of the room at all. I think he believes that Charles killed LaRoche to avenge his friend's death. I don't think the cop knows that Charles was ever blackmailed.

That was my take, anyway. I could be wrong, it's been a while.