Cookson had hoped to be voted in for a second four-year term during the UCI congress in Bergen, Norway, on Thursday.
It is thought that the recent allegations surrounding British Cycling - for which Cookson was formerly president - have tainted his reputation among voters.
A UCI vice-president and president since 2013 of the European Cycling Federation, the UEC, Lappartient is also a former president of the French Cycling Federation and was a key supporter of Cookson during the Briton's run for office in 2013.
It is the first French president of the UCI for the past sixty years, and the mandate of Achilles Joinard.
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Having put ambitions in domestic politics on hold, the Frenchman must now deliver on the wide but often vague promises he made during an acrimonious campaign.
Cookson came under fire this year after a United Kingdom anti-doping investigation was launched into Team Sky and former Tour de France victor Bradley Wiggins.
As the company behind the Tour de France, Vuelta and several other major events, ASO has often been at loggerheads with the UCI over the federation's attempts to create a more cohesive, global calendar, and spread revenues more evenly - Cookson's relationship with the family-owned business was no different.
Lappartient also promised to push for bans on some medications.
Cookson had claimed last week that former president McQuaid had been "lobbying against him", and now it certainly appears as though Lappartient had strong support among the UCI's member nations. It found collusion between Armstrong and the UCI.
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