David Coulthard gave the new McLaren a vote of approval after producing his best qualifying performance of the season at the French Grand Prix.
"Obviously we've got to be pretty pleased with the result of the session," said the Scot, who was third.
"The fuel level was where we would expect to be with the old car, so we've definitely made a step forward. Hopefully we can have a good race."
His team-mate Kimi Raikkonen was ninth after making a series of errors.
McLaren are hoping the new MP4-19B will rescue what has so far been a disastrous season.
It is effectively an all-new car, with a new monocoque, fundamentally revised aerodynamics and modified engine compared to the MP4-19 that started the season.
"Any car that is doing a lap time is fun so it was fun today.
Now, hopefully, we can see a strong race tomorrow, get some solid points and start building from here," Coulthard said
"Obviously we need to wait and see what the race gives us because if we are significantly lighter than everyone else on the grid that won't be good. But I would be surprised if that was the case."
Raikkonen accepted the blame for his poor position.
"Unfortunately I pushed too hard at the first corner and got a bit of understeer, which cost me some time," the Finn said.
"I tried hard to compensate for this on the rest of the lap, which resulted in a few minor mistakes costing me even more time.
"I think it's obvious to everybody that the car shows potential, and I feel very confident when driving it. I'm sure the car's competitiveness will become clear in the race."
McLaren boss Ron Dennis said: "Both our chassis and engine performance have taken a positive step forward, which hopefully will manifest itself in better results for the rest of the season."