Grant believes working alongside Smith can have a positive impact on his own development as well as the team's.
Speaking in The Scotsman, Grant said: "He really does things differently, which is great and probably what I was after at this stage of my coaching career. A lot of teams do the same thing in rugby, follow similar programmes. But it's been different here, which has been great and positively different.
"As for the players, I always had the perception they were really good. Obviously, champions [in 2024], a high-performing team. And that's lived up to it. They seem a really mature bunch, regardless of their age profile.
"I think a lot of it comes from Franco as captain of the ship and steering things and the culture. They are mature because there's a lot of responsibility given to them and there are experienced players here, internationals and Lions."
Grant's most recent coaching job was in Tbilisi where he worked alongside Richard Cockerill preparing the Georgian national team for their summer Test against Ireland. Before that he served as forwards coach at Ulster over a five-year spell from 2019 to 2024 in addition to his time on the coaching staff at Edinburgh.
Grant played 138 competitive games for Edinburgh but he's quickly getting used to life on the other side of the M8.
"I think when you mature in life, when you get older, things change and pro sport is pro sport," he said. "I suppose one thing with me is I really enjoy working with a group and the more you're tight with a group, those are the people, regardless of jersey or country, those are the ones you want to do well and care for."
Grant says he's looking forward to the 1872 Cup double-header over the festive season.
"I can't wait. I'm a proud person and anything you do you want to be proud of, give your best and be competitive. We're all competitive. You want to win. So I can't wait for that game.
"It was the same when I was with Ulster playing against Edinburgh. Couldn't wait. Loved beating them. But it comes from a place of passion, I suppose, and care for the people that you're with and care for your craft, trade, job, teammates. So I'm really looking forward to it."