According to TMZ, they told Khlo that they believe he was hooking up with a girl during his trip to Dubai. He did meet up with Khloe's sister Kim Kardashian while he was there, so everything seemed cool, but apparently Kim said they were only together very briefly and now they're worried that Kim was actually the decoy.
While they've asked Khloe to kick French to the curb, Khloe sees it differently saying they're not exclusive, so who cares who he hooks up with? Even if he DID get together with someone there, it sounds like he and Khloe are just friends with benefits, so it's not cheating either way.
She also wants them to stay out of her business, which makes sense. Having to have a family discussion about being friends with benefits is right below 'root canal' on our "Things We Never, Ever Want to Do" list.