Antoine Griezmann's penalty miss was all that marred a dominant display from the world champions, who were without Kylian Mbappe and Paul Pogba in Paris.
Coman's second international goal got France up and running in the eighth minute, with Olivier Giroud doubling the hosts' lead prior to the half-hour.
Griezmann failed to convert an international spot-kick for the first time soon after, but made amends with a sublime assist for Coman to double his tally midway through the second half.
Substitute Jonathan Ikone helped himself to a debut goal late on, as Didier Deschamp's side – who conceded through Sokol Cikalleshi's penalty late on – moved back to the top Group H in style.
France were quick to compound Albania's frustration – Coman prodding in after latching onto Raphael Varane's exceptional throughball.
Giroud should have made it two with a close-range header four minutes later, but he made no mistake with his next chance, sweeping home from Lucas Hernandez's cross.
Mergim Mavraj's foul on Hernandez handed France a chance to make it 3-0, but Griezmann's spot-kick crashed off the crossbar.
Ardian Ismajli made a last-ditch block from Thomas Lemar's effort after the restart, while Thomas Strakosha frustrated Griezmann.
But Griezmann found a way through Albania's defence again in the 68th minute – drilling an exquisite cross into Coman, who finished excellently on the turn.
There was time for more action, with Nabil Fekir playing in his fellow substiute Ikone for a debut goal, before Cikalleshi snatched a consolation following Hugo Lloris' foul.
What does it mean? Les Bleus look in good shape
France's slip-up against Turkey in June seems to have served as a warning sign to Les Bleus' stars, who hammered Andorra in their last outing and showed no signs of complacency against weaker opposition on Saturday.
Les Bleus are now on 12 points, level with Iceland and Turkey, and they should have no issues in pushing on to secure qualification from their remaining five fixtures.
Coman fills in for Mbappe
With Mbappe out injured, Coman took on the role of being France's main goal threat from out wide and excelled. The Bayern Munich forward displayed fantastic skill and composure for both of his goals, and was unlucky not to add at least one assist, given the chances he created for Giroud.
Albania's troubles on the road rumble on
While Albania were always going to be hard pressed to get a result in Paris, they offered little resistance, and Edoardo Reja's side are relying on maintaining their form at home – where they have won two qualifiers so far this campaign – to give them a chance of progressing.
France should have no concerns over maintaining their winning run when they host Andorra on Tuesday, while Albania face Iceland.