Murray cruised through his opening match against Argentine qualifier Facundo Arguello in straight sets and will now face Portugal’s Joao Sousa on Thursday for a place in round three.
If he beats the world No 44, Murray may face Spain’s David Ferrer, who he has never beaten on clay, in the quarter-finals before a potential last-four clash with either Novak Djokovic or Rafael Nadal.
The British No 1 has won his last 10 matches on the red surface, including titles in Munich and Madrid, and Courier believes the key to his success is trusting his attacking weapons as much as his defence.
“What we saw in Madrid was very enlightening and hopefully it was enlightening for Andy too,” Courier said.
“It looked like he was playing physically on fumes – playing so many matches meant he didn’t really have his legs underneath him in the semis against Kei Nishikori.
“That forced him to play very aggressive tennis and I think against those types of players he needs to do that a lot more.
“We know his defence is as good as anybody’s, his defence is amazing, but I’d like to see him trust his offence as much as he does his defence.
“When he did that in the semis and the final in Madrid, the results were clear – he played some of the best tennis he’s ever played.
“Against the top players you cannot win by defence alone. They just don’t beat themselves.
“You have to attack them. That’s what Andy did in Madrid, and I hope he will do that at this tournament and through the rest of his career.”
Murray is yet to win the French Open, losing last year’s semi-final to nine-time champion Nadal. He has also struggled recently against Djokovic, who has won the pair’s last seven meetings.
Courier, however, who lifted the French Open title in 1991 and 1992, insists Murray is a realistic contender this year for the Paris crown.
“If I were Djokovic or Nadal I would think of him as one of the top, top guys – he’s proven he can win majors,” added Courier.
“Not many players have been able to do that in this era so there must be a tremendous amount of respect for what he’s done and what he’s capable of doing.
“He’s made it to the semi-final of this tournament before, he knows how to play on clay. It’s not a foreign surface to him, it’s not his best surface, but it’s a surface he’s capable of doing exceptionally well on.
“If he was in the other half of the draw, he would have been my favourite to make the final.
“But the draw breaks the way it breaks and there’s no way it won’t be one of Djokovic or Nadal in the semi-final if he gets there.”