The Scot reached the semi-finals in Paris in 2011, has twice made it to the last eight and has always said he knows how to play on clay. However, Murray is aware too that winning at Roland Garros while Rafa Nadal is on the scene and Novak Djokovic is fighting is another thing altogether.
Murray does not have to win here this fortnight for it to be considered a success - defending his Wimbledon title is surely his main aim this year - and he is happy to be in the field full stop, having missed out last year to allow his aching to back recover.
Yet at various stages in his career, the Scot has shown he can play on a surface he only really got to grips with when he trained in Barcelona as a teenager, having grown up playing in Dunblane.
Courier was the kind of doughty fighter Murray would have admired back then and the French Open champion of 1991 and 1992 believes that the Scot's confidence should be rising after he pushed the world No.1 Rafa Nadal to the limit in the semi-finals of the Rome Masters last weekend.
"Andy's played awfully well on this surface," said Courier, who is working at Roland Garros as a commentator for ITV. "His match against Rafa was very, very good and I think he has every reason to feel positive about his game coming in here. I would think he's especially pleased with how his body is feeling, if it feels as good as it looked in Rome. It looked like he was at full strength again."
Though he has no experience as a one-on-one coach, Courier might have been someone who Murray would have considered as a possible replacement for Ivan Lendl.
Courier told Herald Sport that Murray's new coach would not be him, that they had not spoken about it and that he was as interested as everyone else to see both who it would be and when the announcement would be made.
Yet Courier would have made an excellent coach for Murray. As a player, he loved to win but got the best out of his limited ability, something he would readily admit; as a pundit he is considered, analytical and not afraid to tell it like it is.
It is often said of Murray that he is at a natural disadvantage at the French Open because he did not grow up on clay, a surface which demands outstanding movement that needs to be learned over time. While Nadal, Djokovic and Roger Federer do not have to change their styles for clay, Murray does; his flatter ball-striking not well-suited to the slow surface.
Yet Courier believes that Murray's movement - a strength on every other surface - is not the main issue holding him back, if there is one. "His movement's quite natural, probably because of the years he spent in Spain, training," Courier said. "It's not a movement issue for Andy on the clay, but his forehand grip is not ideally suited to this surface because, if he wants to create heavy topspin, he has to work harder to do it with his wrist; he has to risk some timing issues to try to create that punishing, high-bouncing shot.
"It's just not as natural for him. He's certainly not as well-equipped from a grip standpoint as, say, Rafa, for this surface. Probably because of how he grew up playing the game."
The French Open is the only one of the four grand slams to start on a Sunday, making it a 15-day event. As such, the first round is played over three days, a decidedly unfair situation for those playing on day three, as they will be required to win seven matches in 13 days if they want to win the title, compared to seven in 15 for those who play on day one.
Murray has been dealt the bum hand this time round: his first-round match against Andrey Golubev is scheduled for tomorrow.
Seeded seventh, the Scot has won both of his previous matches against Golubev, who was nicknamed the Golden Globule by local press in Australia when he played Murray in the Hopman Cup a few years ago.
With a big-hitting game, Golubev has made a habit of upsetting some big names and beat Stan Wawrinka this year on Davis Cup duty, shortly after the Swiss won the Australian Open in January.
One good omen for Murray is that he also began on a Tuesday when he reached the semi-finals in 2011, so perhaps he will not be too bothered about the later than usual start.