Wayne Rooney scored a tap-in on his return from suspension, although Oleg Blokhin’s men were unfortunate to have not had a goal given when Marko Devic’s shot clearly crossed the line despite John Terry’s impressive clearance.
Hodgson, who has only been at the Three Lions helm a month and a half, believes his team did excellently considering the away-game atmosphere against the Euro 2012 co-hosts.
When asked by ITV if England had exceeded expectations, he replied: "Yes, absolutely, I think they've been really good from the start and that if someone had said we would win the group I don't think they'd have many takers!
"Most people seemed to think we wouldn't get out of the group so we’ve won it and we’ve won it by points rather than goal difference as well.
"That gives us an extra day’s rest which we’re badly in need of and it was a really hard game for us.
"This was an away game with a capital A. There were 60,000 people in the stadium and only 4,000 very brave Englishmen, so we didn't have too much comfort in that respect.
"But I thought it was a really good defensive and disciplined performance and when we needed a bit of luck - when it may have crossed the line - we got that bit of luck and we were able to carry on and actually win the match."
England rarely made forays into the opposition's half in the first 45 minutes, but Hodgson dismissed any notion of tactics being changed to force a winner for the 48th-minute goal.
He admitted: "I don’t think the goal was a result in any real difference in our play but in the first half I thought the shape of our team was good.
"We weren’t really showing enough composure on the ball sometimes when we broke out. That’s still something I think we can work on and improve on.
"This is a fledgling team as far as I'm concerned. We [have] not [been] working together for very long and we are working at our game and showing composure on the ball and showing quality in the attacking areas is always the most difficult part of football.
"And that's why you need your Wayne Rooneys in top form and today's form will be really excellent for him because it's a game he needed."
Speaking of the Manchester United striker, Hodgson was delighted that Rooney was able to score on his return to the side, and insisted the side’s conservative approach for much of the match made sense.
"He's played well, he's worked very hard and in fact he could have had several other goals as well because he got himself into very good positions," he continued.
"I thought on the counterattack we were dangerous enough, but I think we can be even more dangerous than we were today.
"But the important thing of course in these games is you've got to play under the circumstances and we were fully aware all the time that [France] were losing and that a draw would make us top of the group.
"So to some extent you're not going to throw caution to the wind. You're going to be a little bit conservative in your approach because you know how important it is to get out of the group as group winners."