Setting firsts has been de rigeur, as the French might say, in recent years, for Andy Murray; from appointing a super-coach in Ivan Lendl to employing a female coach in Amelie Mauresmo and most recently to winning the Davis Cup for Britain last November.

Each of them have added to the excitement for Murray and the Scot is eyeing another when he begins his title bid here at the French Open tomorrow, taking on 37-year-old Czech Radek Stepanek in the first round.

The French Open is the only one of the four grand slams that Murray has yet to make the final at but on the evidence of the past month, that might be another thing the 29-year-old is ready to change. After early losses in Indian Wells and Miami, Murray made the semis in Monte Carlo, the final in Madrid (beating Rafael Nadal along the way) and then the coup de grace, beating Novak Djokovic to win the Rome Masters last weekend.

For the second year in a row, Murray enters the French Open full of confidence but as the world No 2, he will not have to worry about Djokovic until the final, having lost to him in a tense five-setter in the semi-finals last year.

With a rejuvenated Nadal, chasing a 10th French Open, also in the other half, Murray will back himself to reach the semi-finals at least and though defending champion Stan Wawrinka could be waiting, a first final is a real possibility.

“It would be great to do that, even if I’m a long way from doing that [right now],” said a relaxed Murray. “That is what has been nice for me the last couple of years in the clay season. I have been doing stuff I’d never done before on this surface, so it was nice at this stage in my career to achieve things that I’d never done and maybe thought that I wouldn’t.

“Like the Davis Cup, for example. That was something I never, never thought we’d do and that made it more special. Winning in Rome – I’d had some terrible times there over the years with injuries, with my back – so to win there was amazing.

“This is the only slam I haven’t played the final of, so if I could do that, I would have played in the final of pretty much all the major events in tennis bar Monte Carlo. It would be nice, but I’m not here to reach the final.”

It is a statement that might have seemed outlandish as recently as two years ago. Beaten in the semi-finals three times, Murray always seemed to find one player too much to handle but there is nothing like beating the world No 1 on clay for the first time to lift your spirits.

What was particularly pleasing, to Murray as well, was the way he held his nerve and kept his cool in Rome when Djokovic began playing up, antics that have upset the Scot’s focus in the past.

“I stayed solid the whole way through,” he said. “Any time there was danger, I handled those situations well, I was pretty calm, made good decisions under pressure and that’s what you need to do on clay.

“I was nice and patient, my serve was huge for me, not just last week but through Madrid as well. I need to serve well to beat the best players but I’ve made big improvements on that side of things and hopefully it keeps going that way.”

The biggest improvement of all has been to his second serve, an area of his game that has until lately been a weakness, something every player would look to attack. Now, having made what he describes as “significant technical changes” to his serving technique, he has added pace, spin and direction to his second serve and as a result, he is looking more and more secure.

Was it the influence of his former coach Amelie Mauresmo, whom he split from this month, or the latest addition to his team, Jamie Delgado, who has agreed to travel with him for 40 weeks a year?

“I spent a few days with Louis [Cayer] before Monte Carlo,” Murray revealed. Cayer is the Canadian better known as a doubles coaching guru, the coach of Jamie Murray and the man responsible for bringing through more than 30 doubles players into the top 100.

“I spoke to my Mum a little bit about it, I spoke to one of my friends, Ben Haran, who coaches at Reed’s Academy, which is where Tim [Henman] went. I tried to chat with youngsters about teaching technique. Because a lot of the ex-players don’t know that side of things as much, they’ve never had to teach someone how to serve, they serve fine themselves. It’s easy to say: ‘hit the second serve harder’, but you need to have the technique to be able to do that. By making the changes in my technique and watching stuff online as well and just trying to learn about it has made a huge difference.

“I’m really happy about that. I think it obviously helps me on the clay but I think I’ll get big rewards for that during the grass-court season if I keep improving it and it keeps going that way. It’s been a big positive for me.”

Between times, Murray will be racing home to spend time with his daughter Sophia, who he says is taking after mum Kim, in one way, at least.

“She’s a lot more smiley than me, that’s for sure,” he said. “I don’t know if she gets that from Kim. She has been very calm and chilled so far. I haven’t done anything competitive with her yet, so I don’t know if she is going to have my genes there. Hopefully not.”