Beating Toulon in the Champions Cup at the Stade Mayol "would probably be our biggest achievement to date", says Edinburgh head coach Richard Cockerill.
The capital side top Pool 5, leading Montpellier - who they host in their final group match - by four points.
A win at what Cockerill believes is "one of the toughest places to go in world rugby" would all but seal their qualification for the quarter-finals.
"I'm not worried about going there, I am excited," Cockerill said.
"These are the games you want to be involved in, when you are talking about competing against the very best. We are starting to get a team that can do that.
"We would like to make history on Saturday and be the first Scottish team to win at the Mayol, but we want to qualify out of the pool."
Edinburgh have only ever won twice on French soil in 18 matches in Europe's elite competition - at Castres in 2008 and Racing 92 in 2012, the year the Scottish outfit reached the semi-finals.
Toulon, meanwhile, have only lost twice at home in European competition - to Saracens and most recently Newcastle, in this season's first round of pool matches.
The three-time champions have no chance of qualifying themselves after win just one of their four matches, and are currently languishing in 11th place in this season's Top 14.
But Cockerill, who coached at Toulon in the second half of the 2016-17 season before joining Edinburgh, is adamant the French giants will not lie down in front of a partisan 18,000 crowd.
"I think they will be a lot better than when they came here," he said, referring to Edinburgh's 40-14 victory in the return fixture in October.
"They were in a state of flux, had a lot of injuries and didn't bring anywhere near their best team. But they have got some world-class players and will be much better.
"I know Toulon well enough to know they will never want to lose at home; that will be a big driver for them."
The hosts have Wales scrum-half Rhys Webb, Georgia flanker Mamuka Gorgodze and New Zealand number eight Liam Messam back in harness, and can also call on the likes of All Black backs Julian Savea and Malakai Fekitoa, France centre Mathieu Bastareaud and Fijian flyer Josua Tuisova.
"The quality of their individuals is far beyond what we have got," Cockerill said. "But the quality of our team spirit and organisation and the sum of our parts, as ever, is going to have to be the key decider.
"We don't rely on individuals, we rely on the team, whereas probably they rely on their individual brilliance much of the time."