Colomiers, who reached the 1999 Heineken Cup final where they were beaten by Ulster at Lansdowne Road after winning the Challenge Cup the previous season when they demolished Agen 43-5, believe they are now playing with the sort of confidence to cause an upset.
Connolly's opposite number Jean-Luc Sadourny declared: "We will play our chances to the full at Bath.
"With seven points to make up we will try hard to pull out a surprise result on Saturday - and why not?.
"On Sunday we rediscovered some confidence in our play that had not been there for the last couple of months.
"Bath are a very strong team and we will be putting out our strongest available side.
"We have to work on a number of areas, especially the small details - we conceded two tries from mistakes in our kicking game last weekend.
"We will work on the positive sides of our game such as working the ball out wide. We have to try and unsettle Bath because they are a very structured side."