The two Wimbledon champions - one current and one former - are working together for the grass-court season initially, with a view to a longer partnership.
Considering that the grass-court season includes the small matter of his Wimbledon title defence, it is a trial that could go either way and the fact that a grand slam champion has hired a woman has given his choice an added interest. But Murray, who was coached by his mother, Judy, for several years, is a modern man, thankfully, and quickly shot down a questioner who asked about: "the excitement of having a lady in your corner other than a chap".
"Lady and chap?" Murray echoed, to much laughter. "Man and woman. Let's stick with that.
"Now the decision has been made, it's not something that I'm thinking about. I think it's more about the qualities that she can bring that will help me and my tennis and my team as well. I hope it works out long term because I like her. She's a good person. I hope it works out well."
Mauresmo sat alongside Dani Vallverdu in the Murray support box and applauded more than his former coach, Ivan Lendl, ever did. However, she did not allow herself to get overly excited.
The former world No.1 oversaw practice for the first time yesterday morning and had little cause for concern during the match against Mathieu, who never looked like troubling Murray. The Scot broke in the opening game of the match and after going ahead 3-2 in the second set with another break, he maintained the advantage to set up a match with experienced Czech Radek Stepanek.
The Scot revealed that he had not consulted the rest of his team about hiring Mauresmo, saying that was a conversation they would all share once Wimbledon was out of the way. "With most of the coaching decisions that I've had there is a trial period and it's up to me to make a decision on who that person is," he said. "If it doesn't work, it doesn't work.
"I'll sit down with the guys after I'm finished at Wimbledon and see whether or not we think it has been a good few weeks and whether we think it's something that will work long term.
"Obviously I'll chat with Amelie, too, because it's not just me that makes the decision. If Amelie hates working with me and finds it very difficult being around me, then she won't want to do it either.
"After I spoke to her the first time I just really liked her, for a number of reasons. She was calm. She asked a lot of questions. She listened a lot. I liked chatting to her.
"I decided to sit down and speak to her and had a good chat with her about tennis. I spoke to her a bit about my team and things I wanted to work on. I enjoyed speaking to her. She was very easy to talk to, easy to communicate with. I thought it would be a good time to try it out."
The pair have agreed in principle to work together for up to 25 weeks per year but, with only 11 days to go before the start of Wimbledon, it is unlikely Mauresmo has time to make any big changes to his game. Murray, however, has no doubt that the 34-year-old, who is also France's Fed Cup captain, has the credentials to improve his game. "Away from the court it is really the communication and the relationship that you can build up with that person that is going to decide whether it's going to work long-term," he added.
"In terms of what she achieved on the court, obviously she knows how to win. She was the best in the world. She won Wimbledon and major events. She achieved a lot in her career and I think she's a strong character.
"It's just off the court and when we're having discussions about tennis whether it clicks or not. We won't know just yet."
Elsewhere at Queen's, Jo-Wilfried Tsonga and Stan Wawrinka both progressed to round three, with the latter going through when Marcos Baghdatis pulled out with a shoulder injury. However, Ernests Gulbis was beaten 7-6, 7-5 by France's Kenny De Schepper.