The Norwich City skipper - along with his team-mates - has remained in Malta for a training camp following Sunday's disappointing 1-0 loss to Italy.
And with the Scots having failed to reach this summer's tournament, it will be the players' last game of a long season.
However, it is a very different story for the French who face Gordon Strachan's side in their final warm-up match before they open the tournament against Romania in Paris on 10 June.
And Martin acknowledges they need to improve if they are to avoid back-to-back friendly defeats after struggling to impose themselves on the Italians.
"I think we're disappointed that we didn't show how good we can be, but it's the end of a long season, you have to take that into account," he told BBC Scotland.
"We need to be braver on the ball and show a bit more quality and I think in the second half we did that. We're pleased with how we dug in and showed a lot of team spirit.
"Now we're looking forward to another game against extremely tough opposition.
"Hopefully on Saturday we will be able to put on a bit of a better show with the ball and keep that spirit and doggedness without it."
Martin agreed with Strachan that Sunday's defeat will prove valuable if Scotland again need to counter the 3-5-2 tactics deployed by Italy coach Antonio Conte.
The 30-year-old - who could earn his 25th cap in Metz - also believes taking on opponents of the standard of the Italians and French will benefit the younger players in the squad in particular.
"I think we learned how to play against a difficult system that we're going to come up against in the World Cup qualifying campaign," he said.
"The manager and players have taken quite a bit out of that, but we also learned to be a top team, the kind of risks you have to take.
"We played against a top team on Sunday and I think the young lads, even those who didn't play, will look at those players as something to aspire to, because we have some really good young ones in this squad.
"They have a chance to hit those heights if they want to, if they really want it. It'll show them how hard they'll have to work, it gives them someone to emulate and look up to.
"We need to make sure we can compete with these nations and qualify for a tournament."
Although accepting that the French will likely represent a superior challenge, Martin wants the squad to embrace it and use the occasion as inspiration for the upcoming World Cup qualifiers.
"It'll be a step-up in terms of intensity and tempo I think," Martin said.
"They're obviously the home nation, they've sold it out already and it'll be a taste of what the atmosphere is going to be like at the Euros.
"We'll need to be at it from the start, it's as simple as that and we know that.
"They've probably got a little bit more flair in attack but probably not as good defensively as the Italians so it's a different test for us. We'll go there and we'll have a go."
Scotland defender Russell Martin wants the team be brave when they travel to Metz on Saturday to face Euro 2016 hosts France.