The US Open champion looked comfortable throughout, even in a well-matched first set, and wrapped up victory in 92 minutes on the Parisian hard-courts.
Murray will be particularly pleased with the form of his forehand as he hit a number of winners off that wing against wildcard Mathieu.
"I served pretty well but I struggled a little bit on the return," Murray told Sky Sports.
"The court has got a lot quicker over the last few days so I was struggling a little with the timing and catching it a little late. The ball was staying a bit lower.
"I have never played my best tennis is this event and I would like to change that."
With world number two Novak Djokovic falling to Sam Querrey earlier in the day, Murray is now the highest remaining seed in the draw in the absence of Roger Federer and Rafael Nadal.
Having taken a couple of weeks off after losing to Djokovic in the Shanghai final, Murray took a little time to settle into the match, even being forced to save a break point in his opening service game.
But as the set went on the Scot’s rhythm returned to him and he found things increasingly comfortable.
It took until the 11th game, however, for Murray to fashion himself a break point chance, with more than a little help from a double fault from Mathieu. But there was no luck about the point that sealed the break, the Scot putting up a testing lob which Mathieu completely mis-timed as he tracked back towards the baseline.
Murray almost undid all his good work with a poor game when serving for the set, a couple of errors handing Mathieu a break-back point. But the Frenchman squandered it and Murray took full advantage of the reprieve to seal the first set just a couple of points later when Mathieu hit a backhand into the net.
The early stages of the second set were completely one-sided as Murray broke in the opening game and then again in the fifth.
A small lapse in concentration from Murray handed Mathieu one of the breaks back in the very next game; the Scot gifting Mathieu two break points before capitulating with a poor backhand drop shot attempt that finished comfortably in the bottom of the net.
But Murray, who will next face Poland’s Jerzy Janowicz, quickly regained his momentum and broke to seal the match when Mathieu slapped a double fault into the net.
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