Both previous World Cup meetings - in 1991 and 2003 - went England's way, although France recorded back-to-back tournament warm-up victories over them during the summer.
Ashton said: "We can compete at the same level as France, there is no doubt in my mind about that.
"We shoud have beaten them at Twickenham in August - I know that, and the players know that.
"We will go into the game with every confidence we have a team to trouble the French."
England, despite losing their second pool game in record-breaking fashion to South Africa, remarkably remain on course for a successful World Cup defence.
It is a feat no other country has managed during the tournament's 20-year history.
But with New Zealand and Australia both out of the way, a northern hemisphere team is certain to feature in the October 20 final.
Ashton added: "The South Africa game was a disappointng night for us all, but we knew we had it in us to put in better performances than that.
"The key thing was to knuckle down and start working to make sure that happened.
"Samoa and Tonga were effectively knockout games in our pool, and that bred confidence throughout the camp. There was a big performance waiting to happen.
"We will approach the France game with the same sense of excitement and anticipation that we approached the game against Australia.
"The anticipation going into this game was something I have rarely experienced, and it was no surprise to me they came out and played the way they did."
World Cup fever has now started to grip England for the second time in four years, with optimism replacing the pessimism of three weeks ago.
Ashton said: "It is difficult to have a sense of what is going on back home.
"The only connection I've got is that I had 52 messages on my phone in the first hour after the game, some from people I had never heard of, which is a bit worrying."