The accident happened 24 miles into the 124-mile stage from Colmar to Besancon. Tour organizers identified the victim a 61-year-old woman. Two others were injured when the motorcycle skidded into them.
Serguei Ivanov of Russia won the 14th stage and Armstrong's former teammate George Hincapie rose to second. Hincapie arrived 16 seconds after Ivanov in a small breakaway group.
Hincapie is five seconds behind overall leader Rinaldo Nocentini of Italy. Nocentini was 5 minutes, 36 seconds behind the breakaway group but kept the yellow jersey an eighth straight day.
Alberto Contador dropped from second to third overall. Contador, Armstrong's Astana teammate and the 2007 champion, is six seconds behind Nocentini. Armstrong is another two seconds back.
Hincapie, a 36-year-old American who rides for the Columbia team, entered the stage 5:25 behind Nocentini in 28th place. Through the final miles, Hincapie's breakaway group was more than six minutes ahead of the Italian.
Ivanov made a sign of the cross as he finished the stage after bursting ahead of the breakaway group in the latter part of the ride.
The race enters the Alps for Sunday's 15th stage, a 129-mile ride from Pontarlier, France, to the Swiss ski station of Verbier. The three-week Tour ends July 26 in Paris.