Antoine Griezmann broke the deadlock with a 90th-minute header before Dimitri Payet added a second deep into injury time.
Griezmann and Paul Pogba were surprisingly dropped from the starting XI in favour of Manchester United's Anthony Martial and Bayern Munich's Kingsley Coman as Didier Deschamps' side attempted to attack the Albanians with speed on the wings.
However, France struggled to create quality chances in the first half, with the new introductions creating little danger despite the hosts enjoying the majority of possession.
Albania came close to snatching a lead in the 52nd minute when Ledian Memushaj's effort hit the post, while Olivier Giroud also hit the woodwork for France with a strong header on 69 minutes.
However, just as Albania were looking set to take a point, Griezmann glanced home an Adil Rami cross. The hosts added a second late on through Payet, the match-winner against Romania, with a strike on the counter-attack.
In the earlier game in Group A, Switzerland were held to a 1-1 draw by a resolute Romania in Paris.
The Romanians, who earned their first point of the competition with the draw, took an early lead against the favoured Swiss through a Bogdan Stancu penalty.
Switzerland right-back Stephan Lichsteiner was judged to have taken down forward Alexandru Chipciu in the box in the 18th minute, and Genclerbirligi midfielder Stancu sent Swiss goalkeeper Yann Sommer the wrong way from the spot.
Switzerland, though, struck back after the break through a thunderous Admir Mehmedi strike in the 57th minute. From a corner, the Bayer Leverkusen forward pounced on a bouncing loose ball and lashed an unstoppable left-footed shot into goalkeeper Ciprian Tatarusanu's far corner from 12 yards out.
A raking cross-field pass from Hamsik picked out Vladimir Weiss after 32 minutes, who cut inside before picking out the far corner to open the scoring.
And it was Hamsik who repeated the trick shortly before half-time, cutting back on to his right foot and bending a beautiful shot in off the far post.
A header from substitute Denis Glushakov pulled one back for Russia with 10 minutes remaining, but it was too little too late from Leonid Slutsky's lacklustre side.
The result leaves Russia likely to need a win from their final group game against Wales to avoid elimination, while Slovakia, who face England in their final match, now have a good chance of progressing to the knockout stage.