Greece and Portugal also took a lead in their European playoff series while Iceland and Croatia played to a scoreless draw.
The final four European berths in the World Cup will be made final next Tuesday when the second leg of the various series will take place.
Roman Zuzulia gave Ukraine the lead in a match played in Kiev and Andriy Yarmolenko added a penalty kick that made things more difficult for the French, who will host Tuesday's match in Paris.
France could wind up being the highest-ranked team in the world not to make the field of 32 nations that will battle for the World Cup in Brazil beginning June 12. France is currently 21st in those rankings, one spot behind Ukraine.
Greece defeated Romania 3-1 and Portugal was a 1-0 winner over Sweden in the other European playoffs, which involve teams that finished second in their groups during the year-long qualifying process.
Iceland's tie at home with Croatia was a moral victory since Iceland had just 10 players on the field for almost all of the second half. Olafur Skulason was shown a direct red card shortly after intermission.
The final 11 World Cup spots will be filled by the middle of next week. In addition to the four spots from Europe, all five African berths in the World Cup will be decided in the second leg of that continent's playoff series.
In addition, Mexico and Uruguay have all but wrapped up the last two spots thanks to their piling up big leads in the first leg of their intercontinental series. Mexico downed New Zealand 5-1 and Uruguay defeated Jordan 5-0. The second leg of those series will be held on Wednesday.
The World Cup draw will take place Dec. 6, at which time each national team will learn when and where it will play each of its three group games.