Despite his undeniable love for Glasgow, Matthews says he couldn't pass up the chance to fulfil his dream of playing in France, coupled with the security of a three-year deal with Montauban.
Matthews was under contract at Scotstoun until 2027, and says Franco Smith was crucial in helping make the move happen, and he speaks glowingly of the Warriors head coach.
"I was pretty open with Franco and [Glasgow managing director] Kenny Brown from the start," Matthews told Scotland Rugby News.
"There was no smoke and mirrors. That's how it should be because if you start playing games then it can be tricky.
"This is realistically the last big contract of my career, so Kenny and Franco fully understood. They were both absolutely brilliant with me and I always kept them in the loop about how things were progressing. There was a real level of appreciation from my side towards the club for everything they've provided me over the years and there was mutual respect.
"Franco was welcoming of the move because he always says to boys of a certain age that if a great opportunity arrives then go and take it.
"He knows it's a chance to set up your families and make a bit of a living elsewhere and he always says he will never stand in your way. He didn't and he's a real man of his words, which is something that I've got the utmost respect for."
You can read the full interview at Scotland Rugby News