Murray knows better than to take the world No72 for granted, describing the left-hander as an "unbelievably talented guy".
But the 36-year-old, who narrowly missed out on being seeded, has a 114-19 record against French players. Since August 2012, he has won 63 of 68 clashes against them, including the past eight.
In Grand Slams the record is even better: the Brit has won the past 27 matches against French players, and 29 of 32 overall.
His Davis Cup captain, Leon Smith, believes Moutet represents a unique challenge but is confident Murray will be too good.
"Moutet is a bag of tricks, an absolute bag of tricks," Smith told Standard Sport. "I mean, he plays drop shots, I reckon, on average, twice a game.
"He runs incredible, he's got a spinny, lefty forehand, really great feel on the ball. Quite in and out with focus, but Andy is very good against lefties and he's very good against French players.
"When a lefty goes into his backhand too much, then of course he likes it because he can control his backhand extremely well.
"He'll look to overpower him. I think it's a good thing for him to step up in the court and use his physicality against someone who's a very small, tricky player. I think it gives him a good opportunity to get into the tournament."
Murray has made some technical changes to his game since Wimbledon, where he lost in five sets to Stefanos Tsitsipas in the second round.
"He's a thinker," Smith said. "I think at his stage, after what he's gone through, I think he's right to look for some more answers to give a bit of an edge.
"He's spoken quite honestly that he doesn't have as big weapons as some of the other players out here now. So then you've got to try and find other ways. You've got to try and make them miss a bit more. You've got to find their weaknesses.
"He's right to look at different things. And because the game keeps evolving, he's got to go with it."
Murray pulled out before his third-round match in Cincinnati this month with an abdominal injury but has recovered well.
"In practice, I think he has looked good," Smith said. "Serve speed looks normal, he's moving great. Bring it on."