England and Liverpool winger issued rallying call ahead of Monday's Group D curtain-raiser with Laurent Blanc's Les Bleus, and says they have been working on their weaknesses
The Liverpool player is in contention to start for the Three Lions in Donetsk on Monday, alongside Arsenal starlet Alex Oxlade-Chamberlain, and he ramped up the tensions between the two rivals after England's first training session in Krakow this morning.
"I don’t think we fear [France]," he reporters.
"They’re a good team but so are we. We know their strengths and weaknesses and we’re working on them this week.
"France look very good going forward and have got some great individual players but I think on our day, so have we and it’s obviously going to be a tough game for us.
"It’s a great opening game for us to play but we’re confident we can get a result."
New boss Hodgson has had just two friendlies to experiement with his 23-man squad, winning 1-0 against Norway in Oslo and also beating Belgium by the same scoreline at Wembley.
But the former Liverpool manager has had to deal with injuries to Gareth Barry, Frank Lampard and Gary Cahill before the tournament kicks off tomorrow and has remained coy about his starting XI against Les Bleus at the Donbass Arena.
Hodgson must choose from a combination of the dynamic Gunners' attacking duo of Theo Walcott and Oxlade-Chamberlain, or more conservative options such as Downing and Manchester City's James Milner in midfield alongside captain Steven Gerrard, Scott Parker and Ashley Young.
Danny Welbeck also threw himself into contention after sublime finish against Marc Wilmots' side, but it has been reported that Hodgson is likely to stick with Andy Carroll as the lone-striker after handing the £35million Liverpool striker the number nine jersey.
But Downing, speaking after this morning's training session, insisted it is a great chance for younger players to stamp their mark on the new-look side.
"We've been unlucky in the two friendly games with losing Frank and Gareth," he added.
"They're two big players and they created a lot in qualifying, so it’s disappointing but it’s a chance for others to come in and stamp their mark."
"The team has been relaxed in training and it hasn't been tense around the place.
"Everyone is looking forward to it, obviously a lot of people are saying we won’t get out of the group or we’ll get knocked out further along but I think it’s a chance for the lads to go out and prove people wrong and go out and show we are a good team and we have got good players."