Scotland secured their first victory over France in ten years when they triumphed 29-18 in their Six Nations clash at Twickenham on Sunday.
After nine successive Six Nations losses, Vern Cotter's charges bagged back-to-back wins for the first time since 2013.
Stuart Hogg scored the hosts' first five-pointer and set Tim Visser up for the deciding try, and Laidlaw kicked 14 points to seal the win.
The result was also special for Scotland as it was their first victory over France in ten years.
Laidlaw, who last week said he would trade his 50th cap for a win against les Bleus, levelled former Scotland loosehead prop David Sole's record for appearances as captain and was delighted with his side's performance.
"This is the reason why we pull on this jersey, and make so many sacrifices," Laidlaw told the Six Nations website.
"It's outstanding at the end to hear 'Flower of Scotland', this win was for us and for the fans. I thought we scored a couple of great tries, in amongst some gritty defence.
"France put a lot of width on the ball, sometimes we had to really scramble and keep France from our line and you could see what it meant for us all.
"To lead this team and to lead them here at Murrayfield will stay with me forever, but it is not about individuals – it's about the team. We spoke about that all week and this team, all the fans, we were literally 'as one' today, it was outstanding."
Man of the match Hogg praised his team's performance and the work put in ahead of the Test.
"The team worked incredibly hard during the week to get that victory and you can see how much it means to us in front of our own fans who were unbelievable today," he said.
"We have had poor performances in the past but to make amends is brilliant and we are looking forward to going to Ireland.
"You do not get many opportunities in international rugby and when we created them we took them well in the last two games."