Within three minutes, Christopher Nkunku had a glaring chance to give France the lead, as the ball fell to him at the back post, but his effort was well-saved.
Iceland enjoyed a fine spell midway through the first half but Michael Olise caused panic in the backline with a wicked free-kick delivery just past the half-hour point, as goalkeeper Elias Olafsson flapped at the delivery and conceded a corner.
But it was a wicked delivery from the home side that proved decisive, as France failed to deal with a free-kick conceded by William Saliba - the ball appeared to get caught under Eduardo Camavinga's foot - and Victor Palsson was alert enough to poke the ball beyond Mike Maignan, prompting a remarkable reaction in Reykjavik.
Before half-time, Jean-Philippe Mateta's shot from point-blank range was cleared off the line, after Olafsson saved a fine header from Michael Olise.
On the hour mark, Nkunku had another huge chance, again at the back post, again from a set-piece, but his effort was wild, and flew high into the Icelandic night. He would not be denied, and within minutes, he equalised, as he cut in from the left flank and fired into the bottom corner.
France completed their comeback in the 68th minute, as substitute Maghnes Akliouche found Mateta, who finished from close-range, scoring his first France goal.
Amazingly, within 60 seconds, Iceland were level again, as Albert Gudmundsson sprang beyond the offside trap and fed Kristian Hlynsson, who powered a finish high into the roof of the net.
Both sides felt they could win the game, but neither were able to do so, as Iceland held out to earn a valuable point.
GOAL rates France's players from Laugardalsvöllur...