Charles Leclerc (24) remained Max Verstappen's (24) closest challenger but the Ferrari driver is now 63 points behind his Red Bull rival, with 10 races remaining, thanks to a mistake of his own making.
Should Verstappen triumph in Hungary next weekend, he will go into the August break at least 70 points clear -- meaning that even winning every remaining race may not be enough for Leclerc.
It would take a turnaround of seismic proportions, and Ferrari have a record in recent years of flattering to deceive, but team boss Mattia Binotto (52) was defiant rather than downhearted.
"It has been a good weekend in terms of pace, the car has proven to be very competitive," he told reporters at Le Castellet.
"Charles got the pole, he was leading the race. I think we had an edge on the Red Bull in terms of tyre degradation... I think we come out from here with confidence in our package, our drivers' capacity and our speed."
Binotto pointed to Hungary as another hot race where Ferrari, who had Carlos Sainz (27) race from 19th to fifth in France, expect to be strong.
"There is plenty of reason why we need to smile. Our objective should not be winning but a one-two," he said.
"There is no reason why not to win 10 races from now to the end. I like to be positive, staying optimistic. Could something happen to Max and Red Bull? It already happened to them, as it happened to us.
"But I am not counting on it. I think we need to focus on ourselves and do our best."
Verstappen has won seven races this season to Leclerc's three, while Red Bull have won eight to Ferrari's four.
Leclerc has had three retirements, all while leading, to Verstappen's one.
Ferrari have looked vulnerable on strategy and Leclerc is increasingly facing questions about whether he is too error-prone to sustain a championship bid.
The Monegasque was quick to blame himself, saying his mistakes in two races -- Imola and France -- accounted for 32 points of the deficit.
Ferrari, who last won a title in 2008, have also let him and Sainz down with mechanical failures and some questionable strategy.
"It is a bit of an unfair judgement," said Binotto when asked about Leclerc's mistakes.
"I think that may happen when you are driving to the limit... there is no reason certainly to blame him.
"We have always seen that Charles is reacting very strongly and well when he is doing mistakes and I am pretty sure he will be back in Hungary stronger and hungrier."
Verstappen, the reigning champion, has had his share of crashes in the past but makes very few now and also knows how to play the long game, when to push and when to bide his time.
"These mistakes are easily made," said the Dutchman. "I feel sorry for him of course, it's not nice. He knows that. We have still a lot of races to go and there will be a few tough weekends for us as well."
