Brunel is looking to improve on last season's fifth-placed finish, which was achieved with a 13-6 victory over Scotland in their last game.
Italy also won plenty of plaudits after almost shocking England, before eventually going down 15-9 defeat in Rome.
Those encouraging displays were followed up with promising outings against New Zealand and Australia and a win against Tonga in the autumn internationals.
Italy claimed their first ever RBS 6 Nations win over France at the Stadio Flaminio in 2011 with a 22-21 victory - and Brunel believes his side must show similar desire against the 2011 World Cup finalists this weekend.
"One of the biggest challenges that I have is convincing the players of their own ability and potential to challenge the best teams," said Brunel.
"We still have a lot of things that we need to improve.
"But a lot of it comes down to the ambition that you have, the spirit that you show and how you show it.
"We are looking more to impose our game on our opponents than to just simply oppose them.
"Even if you manage to oppose the rival team in determined fashion, at some point or another you start to suffer."