The striker, who has three caps for France, dribbled past St Etienne keeper Jeremie Janot at the end of a swift counter attack to poke the ball into an empty net on the stroke of halftime.
Briand then doubled his tally by heading in a Jerome Leroy cross three minutes from time.
St Etienne, who knocked out Girondins Bordeaux in the previous round, rarely came close to breaking down the second best defence in Ligue 1.
Ligue 2 high-flyers Boulogne-sur-Mer advanced with an upset 3-1 home victory over top-flight Caen.
Boulogne, third in the table, struck through Alexandre Cuvillier, Steven Mouyoko and Gregory Thil, with France striker Steve Savidan heading in for Caen.
NO MAGIC
There was no Cup magic for little Schirrhein against Toulouse as Danish striker Soren Larsen hit four goals in an 8-0 demolition of the seventh division team.
The amateurs, who knocked out Ligue 2 Clermont in the previous round, were no match for Ligue 1 Toulouse in front of a 6,000-crowd at Haguenau stadium.
The match was played 10-km from Schirrhein because their stadium is too small.
Top-flight Lorient needed a Kevin Gameiro goal 18 minutes into extra-time to see off Ligue 2 Tours 2-1.
Ligue 1 leaders Olympique Lyon set up a mouth-watering last-32 tie with Olympique Marseille after an Anthony Mounier double led them to a 6-0 win at amateurs Concarneau.
The game was originally due to be played earlier this month but was postponed due to a frozen pitch.
There are two all-Ligue 1 clashes on Sunday, with Le Havre taking on Le Mans and Nice travelling to Monaco. Cup specialists Paris St Germain also visit fourth division Ajaccio GFCO.
The draw for the last 16 will be made on Sunday.
