The skipper was helped from the field after just 25 minutes in Paris with Price brought on to replace him.
That was just the second international appearance for the 23-year-old - who made his debut against Georgia in the autumn - but he is confident he can ably fill in if Laidlaw is not fit for the clash with Wales at BT Murrayfield in just under a fortnight's time.
"I'd relish the opportunity to start against Wales if Greig doesn't make it," explained Price. "We will need to see how that progresses.
"But yes, I'd love to play - especially with the game being at Murrayfield.
"I'd be ready. If I was called upon to start I'd be prepared and ready to go. I would obviously speak to the coaches and I'm confident I'd be in a good place for that game.
"I've been ready to go in every game and against France I got my chance, probably sooner than many people thought. But I was ready, I've always been ready."
Scotland came mightily close to a first win in Paris for 18 years - eventually leaving with a losing bonus point - leaving Price with mixed emotions.
And while the No.9's international experience may be limited, he says the presence of Glasgow Warriors team-mate Finn Russell outside him helped ease the transition against France.
"Finn took more of the calls on when I came on - that's what happens when we play together at Glasgow," added Price.
"He was calling the plays off the line-outs and along with Jonny Gray we all had an understanding of what was happening.
"We went to France to win. We knew we had to raise it a level after the Ireland performance but we really felt we could get the win.
"That's why we're so bitterly disappointed. We gave them too much easy ball in the second half.
"They were able to get their hands on the ball and pulled away with two penalties at the end.
"It's an opportunity lost. We've come back with a point but could it have been more? Yes."
Scotland won three matches in this year's Championship
24 March 2017, 3:33pm
Scotland secured three RBS 6 Nations victories for the first time since 2006 as they beat Ireland, Wales and Italy at BT Murrayfield. Here we take a look at what lies ahead for the Scots in the next 12 months.