There were mixed fortunes for the French stars in Marseille on Monday, but sixth seed Benoit Paire advanced.
Gael Monfils is two victories away from winning the Open Sud de France for a third time in Montpellier.
Belgium's David Goffin joins a strong French contingent in the quarter-finals of the Open Sud de France after overcoming Alexander Bublik.
A three-time champion in Montpellier, Richard Gasquet defeated Gilles Simon in the Open Sud de France, but Grigor Dimitrov dropped out.
Roger Federer will not face the familiar foe of Stan Wawrinka as planned after the latter withdrew from the Swiss Indoor Basel.
Former world number one Andy Murray recorded a straight-sets win for just the second time since August at the European Open in Antwerp.
Richard Gasquet lost for just the second time in nine career meetings with Benoit Paire in an-all French clash in Metz.
After dropping down to the Challenger Tour for the second time this season, Jo-Wilfried Tsonga hit the ground running in Metz.
Daniil Medvedev was a set down against Novak Djokovic, but he rallied to stunning 3-6 6-3 6-3 semi-final victory in Cincinnati on Saturday.
Daniil Medvedev and Novak Djokovic will meet in the semi-finals, while David Goffin and Richard Gasquet are set to clash.