Champions PSG, bidding to win the competition for the fifth year in a row, went ahead against Pontivy with a first-half own goal and Brazilian forward Neymar made it two 20 minutes from time. Kylian Mbappe added the third from the penalty spot before Julian Draxler completed the scoring.
The biggest shock came when Olympique de Marseille were knocked out 2-0 by fourth division amateur side Andrezieux.
Their ground was so small that they moved the game to nearby St Etienne but even without home advantage Andrezieux were too good for Marseille and won with a goal in each half.
The defeat extended Marseille's winless run to seven matches in all competitions and they were not the only Ligue 1 side who failed to advance.
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Girondins Bordeaux lost 1-0 at home to second division Le Havre, Ebenezer Assifuah getting the winner. Montpellier, fourth in Ligue 1, conceded a goal in stoppage time to lose 1-0 at third-tier Entente SSG.
Angers also lost to an amateur side, beaten 1-0 by Viry-Chatillon, while Nimes Olympique were hammered 3-0 by Lyon Duchere.
Among the Ligue 1 clubs who did reach the next round were Olympique Lyonnais, who beat lower league Bourges 2-0, and Stade de Reims, who overcame Lens by the same scoreline.
Basement club Guingamp won 4-2 at Stade Pontivyen and second-bottom AS Monaco also enjoyed a rare win, knocking out Canet Roussillon 1-0.
(Reporting by Andrew Downie, editing by Ed Osmond; Editing by Christian Radnedge)
