Joleon Lescott put the Three Lions ahead with a header from point-blank range after half an hour but Manchester City midfielder Samir Nasri levelled before the break - forcing England onto the back foot for most of the second period. However, France were unable to break their defences a second time, allowing Hodgson's side to collect what could turn out to be a valuable point.
"I've had three games," he said. "I am satisfied with those three games but you don't become a really good team in three matches and 10 training sessions. The French have gone 22 games unbeaten. They've not done that overnight. The longer we play together, the better we'll become too."
Hodgson cannot be criticised for the boldness of his team selection. Manchester United striker Danny Welbeck impressed on his first competitive start and Hodgson's decision to hand 18-year-old Alex Oxlade-Chamberlain the biggest match of his young life was fully justified.
"He deserved it," said Hodgson. "The way he's played since coming into the squad, the performance he gave against Belgium, the ability he has to skip past defenders, which is an important ability to have, is excellent.
"I said to him before the game that this was a big occasion, but there'll be so many more big occasions in the rest of his career so he shouldn't hang himself on this occasion.
"I just wanted him to play to the best of his ability, and remember he had plenty of games for England ahead of him."
Thankfully Hodgson was able to report no fresh injury concerns, other than a snapped Achilles tendon for goalkeeping coach Ray Clemence.
However, as so many of his squad lack recent match practice, he does believe their overall fitness will improve as a result of playing in such searing heat.
"There is no doubt the heat has an effect," he said, "And the earlier you play, the more effect it has. Our team felt the heat, but the French felt it as well. We all have to come to terms with it."