The 64-year-old Hodgson, in charge of the team for just six weeks, called on his squad to show what they were made of to end a dismal run of tournament failures going back to their solitary World Cup win in 1966.
"I just hope my players play as they are capable of playing," Hodgson told a news conference on Sunday at the Donbass Arena.
"We have a team full of major stars in their own teams in a very competitive league. The Premier League is widely regarded as one of Europe's top leagues and I see these players performing week in and week out and playing to the very best of their ability at home.
"My hope has got to be that they reproduce some of that form as a team and as individuals when we get out to the field tomorrow night and in the next matches that follow."
England have rarely been as unfancied as they are going into a major tournament. Injuries to key players, a suspension that will keep Wayne Rooney out of the first two matches, and Hodgson's limited time with the team mean expectations are low.
They also start as underdogs against France, who have not lost for 21 matches since November 2010, and not been beaten by England for five matches since 1997.
"I suppose apart from all that things are looking quite good," a relaxed-looking Hodgson joked.
"It is a stern challenge, we are facing a team in excellent form and 21 matches unbeaten at any level of football, let alone international football is a fine achievement.
Hodgson said that coming into a European Championship or World Cup having good form or bad form was not necessarily a decisive factor.
"It's how your team is going to play on the night," he said.
"How people adjust to the circumstances and most importantly what you can do as a football team is what matters.
"I have full respect for the French team as we should have but we will see what we can do."
Asked if after years of failure, England was still a great football nation or not, a stunned Hodgson replied that it was.
"How far do you want to go back in time?," he said. "1966? I can go back further than that. We started professional football in the 1860s or 1870s.
"You can't accuse us of not being a very serious footballing nation. We're all very much aware that we've not won anything since 1966, you didn't need to remind me of that.
"We have a chance, as one of the 16 teams here, to show how good a team we are. I can assure you we'll be doing our best to prove it on the field of play."
After two 1-0 warm-up wins over Norway and Belgium in Hodgson's first two games, England skipper Steven Gerrard said the players were in fine spirits.
"The squad's really happy. We travelled in this morning and have rested this afternoon and we'll be ready for the French tomorrow," he said.
"It's hot, but it's hot for both teams. We won't use that as
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