A great atmosphere in the camp has been a key feature of Leon Smith’s long tenure as captain and that will be even more important here with no fans allowed due to Austria’s lockdown.
Evans has always shown huge passion playing for his country and he was pumped up throughout a 7-5 6-4 victory over Adrian Mannarino that gave Britain the perfect start.
Norrie then saved two set points in a tense tie-break before clinching a 6-2 7-6 (8) win against debutant Arthur Rinderknech.
The 2-1 victory in the tie means Britain need to beat the Czech Republic on Sunday to be sure of topping the group and staying in Innsbruck for Tuesday’s quarter-final.
France are missing their three highest-ranked players but have the sort of strength in depth Britain can only dream of, with nine players inside the top 100 in singles.
Captain Sebastien Grosjean left out Richard Gasquet, who had played in their opening win over the Czechs, bringing in Rinderknech at number one and pushing Mannarino down to two.
Britain had the advantage in rankings – 12 and 25 compared to 58 and 71 – but the margins are small in professional tennis and this event has already produced several upsets.
Evans and Mannarino had played three times before, all of them close, but the British number two recovered quickly from failing to serve out the opening set and took his opportunity in the second.
Evans, 31, admitted he felt the nerves of contesting the first rubber, saying: “I find it a bit more pressure coming out as number two. Your job is to open up the tie, to set it up.
“There’s no denying they’re a strong, strong doubles team. We go one down, they’re in form, it’s a difficult doubles. No one wants to be sat there 1-1. I want it to be 2-0 and out of there.”
It played out that way thanks to Norrie, who claimed his 51st tour level win of the season against his former college rival Rinderknech, who is another player to have made a big leap forward this year.
The Frenchman could not cope with Norrie’s relentless play in the opening set but hung in well in the second and came agonisingly close to forcing a decider.
“It was tense,” said Norrie. “It was difficult because he was serving well. When he got the chance, he was coming forward, so it was tough for me to get into the rally with him.
“It was another huge win, especially in the circumstances with the pressures of Davis Cup, playing France, potentially qualifying. There was a lot on the line. To beat a player of his calibre was massive for me. I managed to do enough today.”
A 3-0 victory would have put Britain in a very strong position but debutant Salisbury and Skupski were outplayed despite France having to break up Herbert and Mahut, who won the ATP Finals last weekend.
The Czech Republic are the weakest team in the group on paper but they gave France a fright on Thursday and have had two days to prepare for Sunday’s match.
Smith said: “We saw all of the matches were difficult against France. We shouldn’t expect anything different. I think it will be a very difficult tie.
“They’ve had a day’s rest, as well. That’s a benefit. So just going to push hard tomorrow.”