The Three Lions went into the lead in Donetsk through a Joleon Lescott header, however Samir Nasri equalised before the break.
With neither side able to find a winner spoils were shared, and Hodgson was happy with what he saw.
“France don’t panic in the final third so you have to be very disciplined in your defending,” Sky Sports report the national selector to have said after the game.
“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.
“France are one of the favourites in the group.
“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,” he concluded.
In the other game in the group, Ukraine beat Sweden 2-1, with Andriy Shevchenko grabbing a brace for the co-hosts.
England take on the Swedes next on Friday night.
By Gareth McKnight