Les Bleus have been in mercurial form under coach Laurent Blanc, having put together an astonishing 21-game unbeaten run heading into the tournament after a disastrous 2010 World Cup campaign saw them bow out amidst controversy in the group stages.
The French beat England 2-1 at Wembley when the sides last met, but Hodgson insists his players will be fearless heading into the Donbass Arena.
"The players think we can beat France, there's no question about that. There's no fear in that respect," he said.
"In any league, 21 matches unbeaten is an achievement. But I don't get the feeling the players are cowed by the task. They're more motivated in a way.
"It may be quite nice for them to go into a game where people are saying 'it will be tough and France are a better team than you'.
"I would think they'll probably quite enjoy the fact that the 'favourite' position is now being taken from us and given to France. We know we can give them a good game, no question."
The former Liverpool boss is under no illusions that England will be expected to qualify from Group D, despite him having been given just two warm-up matches to analyse his squad.
And with the group's curtain-raiser rapidly approaching, Hodgson has confirmed that he is still yet to decide on whether he will adopt a more cautious approach with the inclusion of Stewart Downing and James Milner, or opt for the youthful exuberance of Arsenal duo Theo Walcott and Alex Oxlade-Chamberlain.
"The choice of wide midfielders and the other centre-forward to partner Ashley Young, they're the ones I've had to give thought to," he revealed.
"We do have competition in those places, and furthermore we don't necessarily have people - due to their experience - who are nailed on in those positions.
"They're people holding their hand up and saying 'pick me'. The back four and two central midfielders are those that shout at me 'you've got to put me in the team'."