He was behind Marc Marquez, Jorge Lorenzo and Andrea Dovizioso but feels he will challenge for honours in Sunday’s race.
Crutchlow was satisfied with his performance even though a mistake in qualifying may have cost him a shot of the front row.
"I'm happy," Crutchlow told media. "Obviously Marc's got a big advantage, but he's got a big advantage on everyone. I felt we should have been a little bit closer, but that's the way it is.
"I wasn't, I was fourth. I still haven't had a front row this year, so I'm a little bit disappointed with not being on the front row, but I think we're in good shape.
"I braked a little bit early in one of the corners where the lap previously, I had braked perfectly for it, and that would have been the difference between the second position and fourth, but that's the way it is.
"I don't like this circuit, I don't like riding here particularly at all, so to be fourth and my fastest lap ever around Le Mans, it can't be too bad," he added.
Having finished on the podium at Jerez and two fourth place finishes, Crutchlow has had a solid start to the campaign as he learns to adapt to the new Honda RC213v.