Roy Hodgson was proud with England's performance after his side earned a point in their Group D opener in Donetsk.
Joleon Lescott scored his first international goal on the half-hour mark but Samir Nasri equalised nine minutes later.
England tired in the second half, but they held France out to secure a point from their Group D opener.
Hodgson said: "France don't panic in the final third so you have to be very disciplined in your defending.
"To finish 1-1 and ask the questions of them that we did, I've got to be happy.
"We kept them at bay and there weren't that many situations in front of our goal where I was panicking in any way.
"And there were a few situations in their third where we would have scored a second goal with a bit of luck."
England face Sweden on Friday but Hodgson, who reported a clean bill of health from the game, admitted the toughest opponents of Group D had been negotiated.
"France are one of the favourites in the group," he said.
"They'd gone 21 games unbeaten before today and people were tipping them to be potential winners of the tournament.
"We can't deny on paper they might be the hardest game, but I've got a lot of respect for Sweden and the Ukraine.
"I've got to be very proud of that performance. Maybe that final ball needs to improve and we were maybe a bit anxious in the final third.
"But there were good signs of a team wanting to do well."
The England boss refused to criticise the display of referee Nicola Rizzoli.
"The referee did OK. It's foolish to start commenting on the referee's performance," he said.
"Sometimes you'll get a bit of luck, sometimes not.
"I know that Steven (Gerrard) was aggrieved not to get a free-kick, but the referee was fair to both sides. It wasn't one-sided."
Who was your England man of the match against France?