The Red Devils head into the return leg of a heavyweight European encounter trailing the Ligue 1 title holders 2-0.
Ole Gunnar Solskjaer has conceded that his side have a “mountain to climb”, especially as they are set to be without the suspended Paul Pogba and a number of injured senior stars.
Shaw, though, believes that anything is possible, with United’s recent away form suggesting that a trip to the French capital should hold no fear.
He told the Red Devils’ official website: “The most important thing right now is that, I know we’re 2-0 down, but we’re so positive and so confident within the team. We have to pull off something special, but I feel that we’re capable of it.
“I am really positive that we can go there and get a result and get through to the next round.”
Shaw added: “Most importantly we need to make sure we don’t concede, especially early on.
“I feel if we get one goal then it’ll make the tie completely different. They’ll feel it and it might change the game completely.
“It’s a long time, 90 minutes, and you never know what can happen if we get that early goal and our confidence goes onto an even higher level.
“I feel we can do it with the way we’re going at the minute, especially away.”
United will be making the trip to Paris buoyed by a thrilling 3-2 victory over Southampton in the Premier League.
That victory has lifted them back into the top four and maintained the impressive form being enjoyed under the guidance of Solskjaer.
Shaw is now looking for a memorable continental performance to complement the domestic showings, with the Red Devils still taking aim at a quarter-final berth.
“We just need to think about the good things we did there and take that to Paris with us.
“We’ve got such amazing attacking players. Players that can create and players that can score wonderful goals and I’m sure we’ll have a strong enough squad.”