The Chiefs head to Stade Charlety for a game that reaffirms just how far they have risen under Baxter's astute direction.
Exeter are also pushing hard for an Aviva Premiership play-off place, while Heineken Cup qualification next season is well within their grasp.
Head coach Baxter, though, is not looking beyond Thursday and an opportunity to see his players test themselves against star-studded continental opposition.
"We are looking forward to it because we know we tend to play well in these big fixtures," he said.
"Every time we have gone into Europe and played against some of these well-established French clubs, we've always put in a big shift.
"That is what I am assuming will happen again this week, so I know if we do perform well over in France it will make the game very interesting."
Baxter has retained the team that accounted for London Irish in last Saturday's Premiership clash at Sandy Park, being able to do so after hooker Chris Whitehead recovered quickly from an ankle injury.
"Thankfully, everybody who we had concerns over has come through 100% fit," Baxter added.
"There are some teams who are probably already looking forward to their holidays, but we are not. Instead, we have a number of games left that we want to win, and this is the first of them.
"We've already had some real challenges this season - not least playing the likes of Leicester.
"We came through two games against them, and we also came through what was a very tough final quarter up at Gloucester.
"I have kind of said to the players that I hope it is tough over there because I want them to look at each other afterwards and say we have come through something special.
"There will be nerves pre-match, but that is to be expected, and when we are like that and we're a bit edgy we tend to focus more and become an even better side."
Stade breezed through their qualifying group, averaging 40 points a game, and they will field a side containing four players who saw RBS 6 Nations action this season in Sergio Parisse, Julien Dupuy, Dimitri Szarzewski and Pascal Pape.
Former England wing Paul Sackey also starts, along with two Australian imports in centre Morgan Turinui and flanker George Smith as Stade look to reach a second successive Challenge Cup semi-final.
And Exeter fly-half Ignacio Mieres, a former Stade player, knows the level of performance required if Chiefs are to clinch a semi-final tie against Toulon or Harlequins later this month.
"Perhaps our greatest strength is that we play for the full 80 minutes - we never give up - and it will need that determination from each and every player giving 100% if we are to win and make the semi-finals," Mieres said.
"With the winner playing away to either Toulon or Harlequins, it will need two wins on the road for us to reach the final, and that is a huge challenge.
"But the recent Premiership win against Gloucester, in particular, gave us renewed confidence, and that could be invaluable with the block of games we have coming up."
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