A brace from Karim Benzema added to Franck Ribery’s opener, with Jeremy Menez adding a late fourth as France’s incisive attacking play proved too much for the Baltic side that missed out on qualification after a play-off defeat to the Republic of Ireland.
In addition to some excellent combinations in midfield and attack, France showed great strength from the bench, with substitutes Menez, Mathieu Valbuena and Olivier Giroud sparking a late rally that saw them snatch a fourth.
France now travel to Eastern Europe for the finals, where they face hosts Ukraine, old rivals England and a resurgent Sweden in Group D.
The match got off to a worrying start for France though as defender Philippe Mexes - off colour since joining Milan last summer - almost gifted the visitors an opener after falling on his backside: fortunately for him, Motherwell forward Henrik Ojamaa fired inches wide.
The Mexes question is the only real issue coach Laurent Blanc faces - his form may be poor but he has a good understanding with defensive partner Adil Rami, while Laurent Koscielny is relatively inexperienced at international level despite a good season for Arsenal.
Blanc's main injury worry is midfielder Yann M'Vila and, while there was a minor scare for Alou Diarra in the opening minutes of the match, he proved himself an able deputy and lasted until after the hour mark.
The opener was some strike too as Ribery chested a high ball to Benzema before spinning on to the Real Madrid striker’s flick, controlling the ball with his first touch before rifling a low drive into the bottom right with his second.
That boosted the hosts somewhat and they started to carve Estonia apart, Yohan Cabaye firing a trademark long shot just wide, with Ribery missing the target and a Benzema cross shot almost diverted into his own net by Taavi Rahn.
Just after that incident Benzema, who has flourished under Blanc and had a fine club season for the Spanish champions, managed to better Ribery’s strike with a wonderful finish after the visitors failed to clear a corner: the ball flew across to the left flank where the former Lyon striker had time to take a touch and unleash a vicious rising drive, Sergei Pareiko barely seeing it as the ball ricocheted off the inside of the far post and into the net.
There were no changes for the hosts at half-time and, within a minute, they were 3-0 up, although it was a more orthodox goal as Ribery swung in a low cross that Benzema bundled home from close range, his 17th international goal at the age of 24.
France were having fun now as Ragnar Klavan denied Samir Nasri a simple finish with a superb slide tackle, while Beznema forced a low save from the overworked Pareiko, who at one point tried to waste time as he attempted to slow the onslaught on his goal.
Estonia did have the odd half-chance on the break, Sander Puri forcing a low stop from Hugo Lloris and Vladimir Voskoboinikov hitting the post after a superb pass from the impressive Vassiljev.
But it was France’s party and wholesale changes sparked them back into life in the latter stages as Menez came close to a wonder goal when he left the defence for dead before blasting over the bar, while Valbuena's mazy run and show saw Pareiko spill the ball into Giroud's path, the Montpellier man slipping as he missed what would have been a sure goal.
Giroud made up for his lack of balance when, as the 90 minutes ran down, he backheeled Patrice Evra's low cross into the path of Menez, who rammed home a straightforward finish, only his second international goal in 14 appearances.
France pushed for a fifth but time ran out and, after displaying a team banner thanking the fans for their support, the new-look Bleus now embark on a journey east that will see them look to banish memories of their World Cup disgrace in South Africa two years ago.