Arscott (right) played a key role in Bristol's match-clinching try
Bristol (6) 17
Pens: Hill (4)
Stade Francais (0) 0
Bristol put in a dogged display to earn a well-deserved win over the French champions at the Memorial Ground.
Two Dave Hill penalties were the only first-half scores as poor conditions made free-flowing rugby difficult.
The second half was no easier for Stade as Bristol pegged them back in their half, denied them any attacking threat.
In the dying stages, Neil Brew and Rob Higgitt pressurised Brian Liebenberg into a mistake and combined to put Brew over in the corner for a clinching try.
Bristol started brightly, with only an unfortunately timed knock-on by David Lemi preventing them claiming the opening try after 15 minutes.
But the home front row's dominance of the scrum gave Dave Hill the chance to open the scoring, and when Sergio Parisse limped off with an unpleasant looking injury to his right ankle, the French side's problems only increased.
Mark Regan was a constant irritation to the Stade pack in the first half, but after the break the French side began to get more into the game.
They were gifted a chance to get back in the match on 50 minutes when Skrela had a straight-forward 25-yard penalty, but it drifted wide of the post.
Hill made it three penalties out of three just after the hour mark, and with time running out, the visitors visibly began to lose heart.
A combination of the conditions and tenacious Bristol tackling, particularly by Andrew Blowers on Remi Martin and Julien Arias, denied Stade's backline any chance to stretch their legs.
With eight minutes to go, Hill's attempted drop-goal was well charged down by Jerome Fillol but just when it looked like a length-of-the-field breakaway could be on the cards, he knocked on, summing up his team's afternoon.
To round off a miserable afternoon for the Paris side, in the closing minutes Liebenberg's pass was intercepted on the half-way line, and Brew and Higgitt ran to the tryline together to ensure the ball ended up touched down in the corner for a try.
Bristol head coach Richard Hill:
"It was probably our best result of the last five years.
"To beat the French champions rates as an outstanding achievement. Our front-row did a superb job, and our defence didn't allow Stade any time on the ball.
"We took a gamble playing against the wind in the first half, but the players worked exceptionally hard to make it difficult for Stade to come back."
Stade coach Fabien Galthie:
"I wasn't surprised by Bristol. They played well in the scrum, line outs and in defence.
"They played with more intensity than us, when we tried to put some more speed in our game during the second half Bristol still kept control."
Bristol: L Arscott; T Arscott, Higgitt, Brew, Lemi; Hill, Perry (capt); Clarke, Regan, Hobson; Winters, Hohneck; Blowers, El Abd, Ward-Smith. Replacements: Blaney, Crompton, Llewellyn, To'oala, O'Riordan, Strange, Taumalolo
Stade Francais: Jeanjean; Saubade, Mirco Bergamasco, Liebenberg, Arias; Skrela, Fillol; Parisse, Martin, Mauro Bergamasco; Papé, Du Plooy; Ledesma, Szarzewski (capt), Montanella. Replacements: Blin, Attoub, Weber, Milton, Charlon, Bouhraoua, Messina.