Fresh from his two goals in Saturday's 4-1 win over Albania, Coman opened the scoring after 18 minutes with a cool finish.
Antoine Griezmann missed his second penalty in three days soon after but teed up Lenglet early in the second half to double Les Bleus' advantage, before Ben Yedder's late third.
The win means France are level on 15 points with Group H leaders Turkey, three points ahead of third-place Iceland.
#EURO2020 Le point 🧐 après six journées 🔢— UEFA EURO 2020 🇫🇷 (@EURO2020) September 10, 2019
• Le top 2 de chaque groupe qualifié direct
• Les 4 autres qualifiés le seront grâce aux barrages établis à partir des résultats de la #NationsLeague 2018/19.
Ça va se tendre à partir d'octobre... 😋 pic.twitter.com/Ge3EsCvpgr
France were far from their fluid best in the opening stages, with their less illustrious opponents comfortably keeping them at arm's length.
They did find a way through in the 18th minute, though, Coman latching onto Jonathan Ikone's pass, taking a touch and then clipping over Josep Gomes.
Moments after pawing away Olivier Giroud's instinctive half-volley, the Andorra goalkeeper had a moment to savour.
Moises San Nicolas pulled down Griezmann in the area in the 28th minute, but the Barcelona forward saw his resulting spot-kick superbly kept out by Gomes.
Perhaps frustrated with his side's inability to break down Andorra's stubborn defence, Raphael Varane tried his luck from 30 yards. Gomes was equal to it, though, tipping over to ensure the visitors went into the break just one goal behind.
France started the second half in more positive fashion and were rewarded in the 52nd minute when Lenglet headed home Griezmann's free-kick from six yards.
Gomes then kept out Coman's header, which looked destined for the top corner, before Moussa Sissoko thumped a header of his own against the crossbar from point-blank range.
Coman then scooped an effort onto the crossbar before substitute Ben Yedder added a third in stoppage time, slotting home after Nabil Fekir's free-kick had been parried into his path.