Archibald has been placed in charge of first-team matters following the departure of Jackie McNamara and Simon Donnelly to Dundee United last week and is set to make his managerial bow against Raith Rovers this weekend.
The Thistle board will meet today to discuss who they will trust to lead the club for the remainder of the Irn-Bru First Division promotion drive, and Paton hopes Archie is given the nod.
He said: "The last few days have been brilliant, the training has been fantastic.
"With Archie coming in, it is a natural progression for him to be manager. All the boys hope he gets the job.
"Scott Paterson has come in and been great as assistant too, we have had some really good, sharp sessions. The boys are loving it so long may it continue.
"The way our team is, we want to play the right way and play nice, attractive football.
"Archie wants us to play that way as well and everything he does in training builds towards that.
"The boys would love him to get the job. Most of the names that are being banded about are there for every job.
"We would like a bit of continuity. He is our club captain and there is nobody that deserves it more than him. The boys are 100% behind him.
"He commands authority."
Archibald was denied his dugout debut last weekend as Thistle's trip to Cowdenbeath was postponed due to a frozen pitch.
It leaves them with two games in hand over league leaders Morton but still five points adrift.
The Ton head to Airdrie while Thistle travel to Stark's Park and Paton is keen to keep up the pressure on Allan Moore and his men.
He said: "The boys were desperate to play last week but it is gone now, and we have another chance tomorrow to go and show how good we are.
"Morton have got the points on the board. It is fine saying we have got games in hand but we would rather have the points so we want to get the games in hand played as quickly as possible."
While Paton and his Jags team-mates have spent the week with Archibald, Jags youngsters Stuart Bannigan and Stephen O'Donnell were handed their maiden call-ups to the Scotland Under-21 side.
The pair have been two of Thistle's key men this season and Paton is thrilled to see his colleagues get the recognition they deserve.
He said: "I am delighted for them. I said to Stuart a couple of years ago to keep his head down and work hard and he would reap the rewards.
"He was getting sent out on loan and was maybe a bit low at times but I always knew he had ability and he could shine in the end.
"That is what he is doing and I'm thrilled for him."