The fixture at Parc Olympique Lyonnais kicked off 45 minutes late after clashes between fans before kick-off.
Lyon face four charges for the setting-off of fireworks, blocking stairways, insufficient organisation and a pitch invasion after a late winning goal.
The Turkish club have been charged for setting off fireworks, the throwing of objects and crowd disturbances.
European football's governing body has not yet set a date for a hearing, at which its ethics and disciplinary body will determine any punishments.
Lyon's charge for insufficient organisation relates to poor crowd segregation, while the pitch invasion charge brought against the club is not for fans entering the pitch before kick-off, which Uefa says happened because Besiktas fans threw fireworks.
Violent clashes between fans at one end of the stadium followed the throwing of fireworks, with Lyon president Jean Michel Aulas approaching supporters to calm tensions in the stadium.
Police had also been forced to intervene in trouble in the city before the game. Authorities had categorised the fixture 'high risk', with about 500 police reportedly stationed at the stadium - more than double the usual amount.
In the previous round, Besiktas met Olympiakos, with both clubs working with Uefa to ban travelling supporters in an attempt to prevent trouble.
Besiktas go into the second leg in Turkey on 20 April 2-1 down, after Lyon came from behind late on to win in France. - BBC -