Parra, who played in the 2011 World Cup final which France lost 8-7 to New Zealand, said the Italians would go for broke against them next Saturday as the French would be the one team the Italians would fancy upsetting.
Parra made the remarks despite the fact the Italians will be missing their one world class player Sergio Parisse, who is recovering from surgery to drain a haematoma, a swelling of clotted blood in his left leg, last Monday.
“Of course we must be afraid,” said Parra speaking at the team's base in Croydon, south of London.
“Italy will throw everything into this match. If they can sow seeds of doubt in one team I think they would choose us.
“What is more it is the first game for both sides in the tournament.
“Thus it is going to be a very tough game,” added the 61-times capped 27-year-old.
Parra, who is not a certain starter as coach Philippe Saint-Andre has opted for Toulon's Sebastien Tillous-Borde in the last two warm-up matches the wins over England and Scotland, said there was no point projecting forward as to how France would fare.
“The best way for things to go wrong is to look too far ahead,” said Parra.
“One has to have the ambition of being world champions but first it is imperative to get out of the pool.”
“That phase starts with this match, which is a huge trap.”
The French will go on to face minnows Canada and Romania before the climax, a potential table-topping decider against Six Nations champions Ireland, who Saint-Andre has yet to beat in four meetings