The Scots have won just three games from the last three Six Nations campaigns - including two against Italy in Edinburgh.
But, after Matt Williams was sacked 11 months ago, Hadden has given the squad a fresh impetus and vitality.
Now 27-year-old Paterson is confident he will be celebrating his 60th cap with Scotland's first home triumph against the French for 10 years.
Paterson said: "We haven't felt this confident in quite some years and we are all just desperate to get out there and play good, quick rugby to entertain the fans.
"We all feel good, fresh and sharp now and there is an air of confidence in the side, which is so important.
"With Scotland, we tend to ebb towards the negative side but Frank has brought in a lot of confidence and you can see that in all of us.
"The big question is how far forward we have come in terms of beating France.
"I certainly hope we have, but Frank has certainly brought a trust in his players as well.
"He can tell us to do something and will let us get on and do it. He makes sure he knows the players very well.
"He's been in Scotland all his career and is a proud Scot, coaching all age groups to get to the top.
"He knows the players' strengths and weaknesses and that is vital."
Scotland gave France a major scare on the opening day of last season's tournament in Paris before the home team ran out 16-9 winners.
The French are traditionally slow starters, but Paterson still believes they will be the team to beat this year.
He said: "Historically, this is the best time to face them, but France, nowadays, are so good they can crush you any time.
"But you have to play them some time so why not first? They are my tip for the championship and we just have to stop them on Sunday.
"France have such a good team that, if you worry about what they are trying to do or plan for what they will do, then they will simply change it.
"We are preparing ourselves to go out and impose our game on them, play our own rugby and try to get some tries.
"At the moment, it is the most open Six Nations Championship for quite some time.
"But, until the first couple of rounds are out of the way, you don't know how it will pan out.
"Momentum is a big thing. If you start well in a tournament which lasts six or seven weeks, then winning early is the key."