Sweden hit back just before the break when midfielder Jimmy Durmaz lashed in an angled drive.
In the group's other game, Andorra claimed a huge upset with a 1-0 home win over Hungary, with Marc Rebes scoring the victor in the 26th minute. "It's a shame for him and the whole team".
The Swedes will be happy to let France have the lion's share of possession this evening, but Sweden coach Jan Andersson says they won't fall into the trap of giving the ball back to them.
"We still have four games - 12 points to play for - and we are going to have to battle hard to reach our goal".
France forward Antoine Griezmann twice headed straight at Robin Olsen in the second half but went closer with a free kick from distance that the goalkeeper scrambled to parry as the beaten Euro 2016 finalists upped the tempo.
Holland moved to within three points of the top two with a 5-0 win over Luxembourg in Rotterdam.
France were below their usual swashbuckling standards and facing a tough Swedish side but the Tottenham man should have been more careful late on in the match.
In today's match of UEFA 2018 World Cup Qualification Sweden and France faces against each other at Friends Arena, Stockholm, Sweden.
Didier Deschamps sent Les Blues out in a 4-2-3-1 formation, with Arsenal man Giroud leading the line after scoring a hat-trick in France's worldwide friendly against Paraguay earlier in the week.
Veteran midfielder Wesley Sneijder - making a record 131st worldwide appearance on his 33rd birthday - slotted in a second after 35 minutes. Bulgaria lost ground in the race for top spot, falling to fourth in the group after losing 2-1 in Belarus.
He chose to take a touch after receiving the ball back, but his punt forward went straight to former Sunderland man Toivonen.