In each of their three previous opening games prior to last night's thumping of Honduras, they failed to score a single goal. Their subsequent fortunes could not have been more diverse.
In 2006 they drew 0-0 with Switzerland but would then go on to reach the final, losing to Italy. In 2002 they began their defence of the trophy - won four years previously on home soil - with a 1-0 defeat by Senegal, and in 2010 they were held 0-0 by Uruguay. On both those occasions they would end up finishing bottom of their group, humiliated and home before the postcards.
In their last four World Cups, then, they have either reached the final or gone out in the first round. When looking for an indication of just what this opening result might mean for their chances further down the line, historical evidence, therefore, is of little use. It tends to be all or nothing wherever France are concerned.
Still, better to start this way than the other. Didier Deschamps, the French head coach, and his players were barely mentioned in the pre-tournament discussions about possible winners, a fact reflected in the 25/1 on offer for a France triumph by some bookmakers.
This comfortable victory over a Honduran side limited both in their ambition and their ability may force some to reconsider that stance. The French will still be considered outsiders behind the likes of Brazil, Argentina and Germany but there are several factors in their favour that would seem to enhance their prospects.
Firstly, they could not have been in an easier group had they handpicked it themselves. They took their time to break down a stubborn, often aggressive Honduras side, but there rarely looked like being another upset to rival that jaw-dropping defeat by Senegal.
Switzerland and Ecuador are the other two teams in the table, making it less a Group of Death more a Group of Gentle Pleasantness. Having now got over their previous aversion to winning their opening match, they should surely go on to coast the group with relative ease.
Secondly, they have good players. Some very good players, in fact. Karim Benzema enhanced his burgeoning reputation by scoring two goals, and creating the other that eventually was credited as an own goal by Noel Valladares, the unfortunate Honduran goalkeeper. That was a notable moment in itself, the first goal to be awarded using video technology after Benzema's shot hit the post, dribbled along the line before bouncing off Valladares and squirting into his goal despite his best efforts to swat it clear.
The use of technology seemed to completely befuddle the commentator - a man, ironically, who used to present a programme about robots - but the final outcome was the right one. Benzema wheeled away to claim it as any striker would but this was not to be his goal. The matchball for a hat trick will need to wait for another day.
Benzema was backed up by accomplished displays from Mathieu Valbuena and Antoine Griezmann, in particular. Missing the injured Franck Ribery, there is no one single shining light in this French side, something that could work in their favour. This is a group being prepared for Euro 2016 on home soil in two years' time but this mature performance suggested they may be capable of a sustained World Cup run as well.
Thirdly, there is a sense of calm behind the scenes and that could also prove vital. In 2010 France made their embarrassingly early exit to the backdrop of in-fighting, a player coup against unpopular manager Raymond Domenech, and extensive recriminations. This time, with Deschamps now in charge, there is said to be more of a family atmosphere among the group, the players all getting on and thinking more about the collective and less about themselves as individuals.
Peace and harmony will not be enough to make them world champions again but not having civil war playing out behind the scenes can only be to their advantage. Liberte, egalite, fraternite and all that.
The result continued the impressively upbeat start to the tournament, a 10th game without a draw. It was perhaps the most dogged to date - despite France eventually scoring three times to keep up the impressive strike rate in the competition - and the first real example of a side showing a determination to sit in and spoil rather than looking to get forward.
Honduras, who included Celtic's Emilio Izaguirre in their line-up, will not have won many new friends with some tackling that was ferocious to say the least. They could point to the decision to only show a yellow card to Paul Pogba for a wild retaliatory swipe at Palacios with his boot as evidence that it was not only one side dishing it out but this was not a night when they enhanced their reputations.
France, on the other hand, are up and running. Goodness only knows what will happen next.