Their opening victory of 30-12, was courtesy of tries from Man of the Match Rynard Landman, Ollie Griffiths, Adam Hughes and Matthew Screech.
The Men of Gwent will travel to Castres in the hope of claiming another win, similarly to the double they did over fellow French side Stade Francais during last seasons competition.
Director of Rugby at the Dragons, Lyn Jones commented: “There are four really strong teams in this group and we travel to Castres appreciating that if you want to do anything in this competition then you have to go to France and win a game of rugby.
“We've got two opportunities and after starting with a bonus point win it's important that we go to Castres and get something from our journey.
“It's a massive challenge but winning out in Stade Francais last year and scoring four tries gives us confidence and understanding that we can do it.
“We have nothing to lose and we need to drag them into a game of rugby and play to our strengths.
“We were positive and I am really pleased for the players because we have been developing and growing for a few weeks.
“We got the mix of our game right, we played with tempo, speed and accuracy.”
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