Les Bleus put three past Gibraltar without reply on Friday night to remain perfect in the section, while Gus Poyet's men sunk the Republic of Ireland 2-1.
Barring a brief scare when Gibraltar's Ayoub El Hmidi tried to channel his inner David Beckham with an effort from the halfway line - which landed on the roof of Brice Samba's net - France were unperturbed en route to a straightforward if not sensational triumph at Estadio Algarve.
All-time top scorer Olivier Giroud increased his Bleus tally to 54 with a header inside the opening three minutes, before a Kylian Mbappe penalty and Aymen Mouelhi own goal sealed the deal for France, who have begun the road to Germany as they mean to go on.
Having also kept clean sheets in victories over Ireland and the Netherlands in March, Didier Deschamps's men are sitting pretty at the top of Group C, three points better off than Greece having played a game more than their upcoming opponents.
Yet to concede a goal in Euro 2024 qualifying, France have redemption on their mind for next year after their humbling last-16 exit from Euro 2020 and agonising World Cup final defeat to Argentina, and righting those wrongs may very well have been a big factor in Deschamps's decision to stay on until 2026.
Les Bleus welcome Greece to Saint-Denis aiming to prolong their unbeaten home run in Euros qualifying to 11 games since a shock 1-0 defeat to Belarus in 2010, but facing a fellow unblemished nation will not be a cakewalk.
Since stunning the continent to lift the Euro 2004 trophy aloft, Greece's attempts to make more waves in major tournaments have often ended in abject failure, but Poyet has already made great strides in his efforts to guide the world's 52nd-ranked nation back into the big time.
Having posted their own routine 3-0 win over Gibraltar in their opening battle, Greece were indebted to an Anastasios Bakasetas masterclass during the visit of Ireland, as the captain blasted home a penalty before setting up Georgios Masouras for a fine finish either side of Nathan Collins's equaliser.
While there is still plenty of football to be played in Group B, Greece - who failed to make the Euro 2016 or Euro 2020 finals - owe a token of gratitude to France for Les Bleus' 4-0 win over the Netherlands, as Poyet's side sit above their Dutch colleagues in the second and final qualification spot.
Even if the Netherlands can restore order, Greece have their Nations League success to fall back on - the Pirate Ship earned promotion to League B for the next cycle and could therefore try to punch their ticket to Germany via the playoffs - and the visitors now have five successive Euros qualifying wins to their name since 2019.
However, the Pirate Ship had failed to win in three successive away games before seeing off Gibraltar, and nine of their last 10 meetings with France have ended in defeat, although the one outlier was a historic 1-0 triumph in their Euro 2004 quarter-final.
Lens goalkeeper Samba was awarded his senior France debut on Friday night after AC Milan's Mike Maignan complained of a calf injury in training, and it is unclear whether the latter's participation in Monday's game is also at risk.
Samba should therefore feel confident of keeping hold of the gloves, and Deschamps also lost Ferland Mendy and Adrien Rabiot to injury prior to the win over Gibraltar, but Les Bleus came through that three-goal success unscathed.
Chelsea's Wesley Fofana also earned his first France cap last time out and may have done enough to keep Dayot Upamecano at bay, but Jules Kounde is an option for change over Benjamin Pavard on the right-hand side.
Meanwhile, Greece midfielder Petros Mantalos was apparently taken off with an unspecified injury in the dying embers of their win over Ireland, but it is currently unclear how severe the 31-year-old's issue is.
Poyet could do without any additional concerns in the engine room after Andreas Bouchalakis missed out on Friday night, while Norwich City left-back Dimitris Giannoulis was another notable absentee from that success.
Should Bouchalakis and Mantalos both fail to make the cut, the defensive-minded Manolis Siopis will likely fill the void in midfield, while Buckingham-born George Baldock should continue at right-back for the Pirate Ship.
France possible starting lineup:
Samba; Kounde, W. Fofana, Konate, T. Hernandez; Griezmann, Tchouameni, Camavinga; Coman, Giroud, Mbappe
Greece possible starting lineup:
Vlachodimos; Baldock, Mavropanos, Chatzidiakos, Tsimikas; Bakasetas, Kourbelis, Mantalos; Masouras, Pavlidis, Pelkas
We say: France 2-0 Greece
Despite putting three unanswered goals past Gibraltar, France were criticised for a perceived sense of profligacy in the final third, although such wastefulness can be forgiven after a energy-zapping domestic season.
Greece will certainly be no pushovers on the Stade de France turf, but Poyet's side are yet to face the test of this magnitude and should travel back to base with nothing to show for their efforts.
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