The 'Clarets' made 10 changes from their Europa League qualifying draw with Aberdeen on Thursday, with Irish midfielder Jeff Hendrick the only survivor.
The game was notable for it being Robbie Brady's return from a long time on the sidelines through injury and his dipping free-kick called Benjamin Lecomte into an early save.
Paul Lasne and Sam Vokes both squandered chances, before Brady limped off just before half-time, putting something of a dampener on proceedings.
Both sides had chances to win the game in the second half, with Jon Walters seeing a volley cleared off the line by Pedro Mendes, Kevin Long heading narrowly wide and Isaac Mbenza not quite getting the requisite curl on his free-kick.
The the end, the game finished goalless as focus now returns to competitive action once again for Sean Dyche's men as they face Aberdeen in the second leg on Thursday.