He believes that it is Wilkinson's tireless defensive work that sets him apart from other fly-halves in the tournament.
"Look at how many rucks he [Wilkinson] gets involved in. He is a different type of player to Frédéric Michalak [France fly-half] and Derick Hougaard [South African fly-half], because he's more aggressive defensively and acts as an extra wing forward (loose forward)," said Woodward.
"At the end of the Wales match he was out on his feet."
Wilkinson has been below his best at the tournament and has come under scrutiny for his ability to operate under pressure. Against Wales on the weekend, he was again put on the back foot and looked out of sorts until centre Mike Catt came on in the second half and took the pressure off the England No.10.
Woodward hinted at the fact that Catt's performance against Wales could have earned him a place in the starting XV against France this coming Sunday.
"When Jonny is playing wing forward we need someone to step up and replace him at No.10. Mike Catt did the job against the Welsh," he said.
While the England boss talked up Wilkinson's state of mind and his own team's chances, he did not seem impressed with the form of the French, whom many are touting as favourites for the game following a host of strong performances in the tournament.
Woodward believes that France have yet to be tested in the tournament, despite Les Bleus' comprehensive 43-21 victory over Ireland in the quarter-finals.
"I'm not quite so sure that the French have come on in leaps and bounds. I don't think they have played the standard of opposition we have here," said Woodward.
"Also while they played some fantastic rugby against the Irish they weren't so impressive when they came under pressure whereas we are."
But Woodward did concede that his side had some work of their own to do after a sub-standard performance against Wales.
"We lost a bit of concentration, particularly in the first half [against Wales], which isn't normal. But it wasn't quite as bad a performance as I thought initially," he said.
"However if we don't make a marked improvement we will lose. I did not come out here for us to finish second, third or fourth."