PARIS—Maybe it’s the fact that, by contrast, he looks so. . . well fed—more ham than ham actor. Maybe it’s that with his severe flat-top he looks more like a first lieutenant than a hipster you might find footloose in the Bastille district. Or perhaps that “thumb dance” and the combination punches he throws after a win are a mite too aggressive, or insufficiently “artistic,” for the fickle French.

Whatever the case, Jo-Wilfried Tsonga may have the attention of Parisians, but Gael Monfils has always had their hearts. Tsonga likes to spend time in the country, fishing. Monfils trolls the clubs and streets, just as popular with the under-30 crowd as he is with the older French set. The French love the “bling-bling” of Monfils—the disparaging term was borrowed from hip-hop and coined to describe former French President Nicolas Sarkozy—his spectacular game and his showmanship, but even his staunchest fans will admit, when pressed, that Tsonga has a much better chance to become France’s next, long-awaited Grand Slam champion.

At this moment in time, that’s a self-evident truth. Monfils is back at home, presumably resting from the three physically and emotionally draining performances he logged at Roland Garros last week. Tsonga is still banging away, and now he has to march into the lion’s den, having locked up a quarterfinal berth with yet another uneventful, workmanlike, very un-Monfils-like win over Viktor Troicki of Serbia.

Tsonga won the match, 6-3, 6-3, 6-3, thereby keeping his straight-sets streak alive. He hasn’t dropped one yet at this event and passed this, his toughest test yet, easily. He put 77 percent of his first serves into play and never had his serve broken (he faced just three break points) by a guy who’s built on a comparable platform, two inches taller at 6’4”, but considerably leaner and lighter. “You know, for me it’s easy now, Tsonga said afterward. “Everything is positive. I’m in quarterfinal here in Roland Garros for the second time. I mean, I have nothing to lose, anyway.”

Of course, he would have had more to lose—but an easier assignment—had Gilles Simon managed to upset Federer in the match that immediately followed Tsonga’s on Chatrier. As it was, even the hope that Simon had softened up the No. 2 seed for Tsonga by extending him to five sets were dashed when the winner strolled into the press conference room shortly after the match, looking fresh as a daisy and feeling frisky as a colt.

In between some amusing exchanges with reporters (more on that at a different time) he happily announced: “Now I know clearly how I stand, I feel fresh. It wasn’t like a four-and-a-half hour five-setter, but I’m happy I never felt tired. I always enjoy these battles because they give you information—physically, more than any other way. Sometimes you go through a few tournaments without having a five-setter. I feel good.”

This was probably the first time in history that any player has groused about not getting enough five-set matches, and it suggests that even if Tsonga can force a long match, he can’t count on Federer’s age, or residual fatigue, to help him. Simon wasn’t exactly the best preparation for a match with Tsonga, Federer admitted, but that wasn’t overly daunting. “I think Jo is best on hard courts, but I know he’ll have the crowd with him here, and he’s moving better than he ever has on this (clay) surface.”

Tsonga knows exactly what he’s up against, not just in that intimidating record the all-time Grand Slam champ will bring to their quarterfinal—today’s win was Federer’s 900th; only three men have won more—but also in the specific situation.

“It’s almost another sport altogether,” the Frenchman mused on Grand Slam tennis. “I’m probably going a bit too far in saying that, but we had (Grigor) Dimitrov yesterday. Is he going to fight Djokovic in the Grand Slam? It’s a different thing altogether to fight Djokovic in Madrid, or elsewhere, because you’ve got less mastery, less control of what’s going on, as opposed to here (at a major).”

Tsonga was in an expansive, jocular mood in his press conference, with a firm grasp of what his ultimate mission here is—potentially, to accomplish something he hasn’t done yet: Beat two or more of the top players in successive matches. In this, he was surprisingly forward thinking, but not in an arrogant way: “I know that these are exceptional players. There are not fifty like them. Now, beating one, I know that I’m able to do that. Beating two, well, for the time being, I have never done it.”

Tsonga has two wins over Federer, one of them in a stunning rebound from a two-set deficit at Wimbledon in the 2011 quarterfinals. The man waiting to usher him out of the semifinals that year?—Novak Djokovic, against whom Tsonga had four match points before losing in the quarterfinals here last year.

If Tsonga’s chances have improved since then, it’s on two fronts. His backhand has been more reliable, and he’s not as prone as in earlier years to go soft in a long match, losing that requisite, fierce attention to every opportunity—and every potential pitfall.

“I have been working on my backhand since I was the age of five,” Tsonga said, just half in jest. “And it’s a disaster, my backhand, so I’m working on it. And I have worked on it since I was small, since I began my tennis career. But I’m increasingly solid. I don’t make many unforced errors with it. Now, it’s not the shot of mine that shines. It’s not where I will shine to make good points. But it’s not a shot where I make lots of unforced errors anymore, either.”

Indeed. Tsonga has been firing on all cylinders here, commanding with his serve, lethal on the forehand wing, ever ready to move forward and end points in the forecourt. But will his synapses fire as faithfully, steadily, and consistently as they must for him to go where no French player has gone since 2008, when his domestic rival Monfils made the semifinals?

It’s a good question, and one that leaves even Tsonga uncertain. “I don’t know. I mean, I’ve got no idea. There are so many different parameters to the question. It could be the opponents I have met who weren’t necessarily as good as those I met in previous years, or is it not that? I don’t know. I have got no idea. For the time being I’m just playing my tournament, and, quote/unquote, the real business-like stuff is starting from Tuesday.”

This may be Federer’s 36th straight Grand Slam quarterfinal, but you can bet that Tsonga is hoping that come Tuesday, it will be anything but business as usual at the office.