Les Bleus, who failed to win a game at the 2010 World Cup or Euro 2008, had to settle for a share of the points in a 1-1 draw in Donetsk after midielder Samir Nasri cancelled out Joleon Lescott's opener for England.
Laurent Blanc's team, however, enjoyed a lot of possession and managed 15 shots on target to just one for England.
"We are disappointed not to have won it but glad not to have lost. And we didn't deserve to lose," Blanc said.
"I thought we were timid at the start and I don't know why. England didn't dominate but they had opportunities," he said.
After playing quick, one-touch football in their warm-up games, France looked short of ideas against England coach Roy Hodgson's defensive curtain.
"We don't want to repeat that experience of starting slowly but perhaps it was something we needed to get over. I hope we will be ready from the first minute in the next game," said Blanc.
"We took our time to really start playing and that's a pity. We only found our rhythm after conceding a goal, but afterwards we showed our style," he said.
"We had the ball and we love to have the ball, and so does the coach. We will need to do this in our next match, which will not be easy at all."
"We failed to create enough decisive chances. We did not make it tonight, the English defended very deep, so it was difficult for us to find space.
"We won a good point, and we will have to take the three points during our next two matches," he said.
"With a little bit more accuracy towards the end, we could have won this game," said midfielder Alou Diarra.
