Platini, 63, was head of European football's governing body until being banned in 2015 for ethics breaches.
The former France midfielder and three-time Ballon d'Or winner has always denied any wrongdoing.
Qatar beat bids from USA, Australia, South Korea and Japan in 2010.
Platini is in custody and being questioned in Nanterre, a suburb in western Paris.
Officials have been investigating alleged corruption connected to the 2018 and 2022 World Cups for the past two years and were reported to have interviewed Sepp Blatter, the former president of world governing body Fifa, in 2017.
Platini was banned over a 2m Swiss francs (£1.3m) "disloyal payment" from Blatter, who was also banned from football for his part in the matter. Blatter has also always denied any wrongdoing.
Platini's eight-year ban was later reduced to four on appeal and will expire in October 2019.
Qatar's bid team has been previously accused of corruption, but was cleared following a two-year Fifa inquiry.