The world champions, below-par throughout, looked as if they would struggle to take all three points until a brilliant 25-yard shot from Zinedine Zidane in the 67th minute. With the score level at 1-1, he ran on to a Youri Djorkaeff knock-down and fired a left-footed shot inside the far post.
With the Armenian defence tiring, Lilian Laslandes made it 3-1 six minutes later with a powerful right-foot drive.
The late strikes came as a relief to France after a shock fifth-minute goal by Karapet Mikayelyan. The 29-year-old striker beat the French offside trap and slid the ball past Fabien Barthez from the edge of the penalty area.
That early strike left the world champions - desperate for a win to keep in the hunt for Euro 2000 qualification - stunned and dispirited, but they were handed an equaliser seconds before half-time when Laurent Blanc collected a long clearance from Barthez and was fouled by Vardan Khatchatrian as he was about to shoot. Djorkaeff, who received a hero's welcome from home fans before the match because of his Armenian ancestry, converted the penalty.
Armenia battled to the end and deep into second-half stoppage time scored through a Arnen Shakhgeldyan penalty.
France's victory means that they will be assured of at least second place - and therefore a place in the play-offs - if they win their final match against Iceland at the Stade de France next month. With the sweeper, Sarkis Hovsepyan, outstanding, Armenia looked capable of matching their home draws against Group Four contenders Ukraine and Iceland at the Hrazdan Stadium, and until Zidane's vital strike they never looked at ease and could have fallen behind for again in the 51st minute, when Tigran Yesayan went past three defenders before losing control as he was about to shoot. France's Frederic Dehu was sent off in injury time for a second yellow card.
In the same group Russia edged past Andorra 2-1 away, with both goals coming from Viktor Onopko.
Savo Milosevic, the former Aston Villa striker, took only 10 seconds to score for Yugoslavia in their 4-2 victory over Macedonia in Skopje. The result puts the Yugoslavs two points ahead of Croatia with the two teams due to meet on 10 October in Zagreb in the group decider, which will also have a bearing on the Republic of Ireland's fate. Yugoslavia would need only a draw to qualify for the finals for the first time since 1988. They qualified in 1992 but were barred because of United Nations sanctions over the war in Bosnia. They also were barred from qualifying for the 1996 tournament.
Boban Babunski helped Yugoslavia with a fourth-minute own goal. Dejan Stankovic added Yugoslavia's third with a spectacular volley under the crossbar from the edge of the penalty area in the 16th minute and Porto's Ljubinko Drulovic completed Yugoslavia's scoring six minutes before half- time. Macedonia managed only two chances from counter-attacks in the first 45 minutes, Dragan Veselinovski hitting the post after 20 minutes. In the second half, Macedonia finally broke through with Artim Saqiri scoring in the 59th minute and then Sasa Ciric cut the deficit to 4-2 in the 87th minute.
Igor Stepanov scored a second-half injury time equaliser to give Latvia a 2-2 draw with Georgia in Group Two, but it was not enough to halt his country's elimination from qualifying for the European Championship. The draw left Latvia in third place, four points behind Slovenia with only one more game to play.
Georgia dominated early on and took a 2-0 lead through the Ajax striker, Shota Arveladze, and Mikhail Kavelashvili. Latvia's fightback started after 62 minutes through Imans Bleidelis and they completed it after Georgia's Mamuka Tseretali was sent off after receiving his second yellow card 10 minutes from time.