The 'Ikale Tahi were pipped 23-21 in Kumamoto last night, having trailed 17-0 just before half-time.
Tonga also gave Argentina a 28-point headstart last week and coach Toutai Kefu was at a loss to explain their sluggish beginnings.
"I don't know, it's a good question. The coaches talked about it straight away post-game - maybe we warm up for too long (laughing), I don't know. It's something we need to look at. I think it's probably just the mental thing because, as you can see, we finish a game really well so definitely an issue for us," Toutai Kefu said.
France's two Fijian flyers inflicted the initial blows with Alivereti Raka setting up Virimi Vakatawa for the opening try before regathering his own kick to score the second.
Sonatane Takula struck back for Tonga with 30 seconds to play in the first half, which cut the deficit to 10 points and Toutai Kefu said that gave the 'Ikale Tahi some real belief.
"We didn't start the game as well as we thought we would, very similar to last week, and I think just after half-time the boys realised that, even though we played poorly, we were still in the game. We had 40 minutes to turn that around and I think just mentally we just had a little bit of a mindset change in the second half to keep putting pressure on them with the ball in hand, with territory," said Toutai Kefu.
Malietoa Hingano capitalised on a wicked bounce to score Tonga's second try and close the gap to just three points with over half an hour still to play.
Two penalty goals gave France a nine point buffer with 20 minutes to play but Tonga began to exert real pressure on the opposition line, as the Kumamoto crowd got behind the men in red.
The French defence cracked again with just 90 seconds left on the clock, as flanker Zane Kapeli out jumped Damian Penaud to score from a pinpoint cross-kick from Leon Fukofuka.
Latiume Fosita slotted the sideline conversion to make it 23-21 but France regathered from the kickoff and promptly booted the ball into touch to secure their third straight win and seal a spot in the quarter finals.
Tonga captain Siale Piutau was proud of his side's performance but said ultimately they made too many errors.
"I think it takes a while for us to grow into the game and start to get that belief. I think it just comes too late for us but I think the more times we play tier one nations the better it's going to be for us - we're going to grow in belief and I think just that first 20 minutes France did a great job in keeping us down in our own half and we were making errors, slipping off tackles and eventually that cost us the game," Siale Piutau said.
A third straight defeat ends Tonga's faint hopes of reaching the quarter finals.
It also means the 'Ikale Tahi miss out on automatic qualification for the next Rugby World Cup, with only the top three teams in each group guaranteed a place at France 2023.
Toutai Kefu said despite all the adversity the team and players have gone through they have continued to work hard and improve on and off the field.
"The sacrifices they make just to turn up and to endure what we endure while we're on tour and during our campaign I'm really really proud of them. Definitely proud of what happened on the field - the way where they just stuck in there in the second and be able to fight back to put us in a position to nearly win the game," Kefu said.
First five James Faiva said sacrifice is just part and parcel of representing Tonga, whether players are at the World Cup or not.
"I think there's a lot of players out there too that want to be here but they have to sacrifice for more money for family first but us boys that turn up we just put the jersey (on). We let the boards do their work and we just do ours," James Faiva said.
Faiva said playing consecutive tests against New Zealand, England, Argentina and France has been a steep but valuable learning curve.
"When we first played the All Blacks that was a big step for us and we slowly came into England we started believing (in ourselves) every single game playing a tier one game. If we get more tier one teams during and after the World Cup I think it will help us tier two nations compete," Faiva said.
Toutai Kefu said more top level matches is just one way World Rugby can help close the gap for countries like Tonga over the next four years.
"That brings more quality time together. We also have a list of players that, through some reason or another, are not here...Definitely everyone can see the improvement over the last three weeks - last four weeks if you include that All Blacks game. We've improved out of sight, I think, and still the last couple of games we probably lost it due to our own fault," said Toutai Kefu.
The 'Ikale Tahi will round out their Rugby World Cup campaign on Sunday against the United States in Osaka as they look to finish on a winning note and avoid finishing last in Pool C.