However if they are to make it through to the competition's last eight for the first time since 2007 then they will have to navigate a tricky trip to France.
It has been almost seven years since the Dragons last tasted victory across The Channel but Jones believes there is no better time to right these wrongs than the present.
"I was very pleased with Friday's performance but we are under no illusion to how challenging and difficult Bordeaux-Bègles will be to play against," Jones told the South Wales Argus.
"We will be focussing on our own game. They are strong at scrum and maul but we dominated other aspects of the game."
"You have to be confident in playing the French and English because their leagues can stagnate, based around power and kicking.
"We are a good attacking side. There's a kudos about French teams that they are brilliant but you've got to understand what they are all about - they don't hold any fears for us but we have to be on top of our game."
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