The clashes erupted at a toll gate between fans of Lyon and Paris Saint-Germain (PSG) headed to the evening's match in the northern city of Lille, which Macron attended.
The violence occurred 60 kilometres (40 miles) from Lille, where the final was being played because Paris's Stade de France is being readied for this summer's Olympics.
One bus was set on fire and two others damaged, local Nord department authorities said in a statement overnight, adding that 30 supporters and eight police officers were injured. Fourteen people required "medical attention".
The clashes involved about 100 Lyon supporters and 200 PSG fans, a police source said.
Police prefect Bertrand Gaume said one group of supporters got out of their bus and attacked another carrying rival fans, who threw smoke bombs.
"There were very violent brawls" before police intervened, Gaume said, adding that one bus was left burnt out.
Mingling with the public in nearby Tourcoing ahead of the game, Macron said he "condemns all violence with the greatest firmness."
Heavy security
Traffic on the major north-south A1 highway was interrupted in both directions.
The supporters' group Paris Ultras Collective said in a statement fans of the two clubs had been supposed to take different routes to the match, but Lyon fans attacked a bus carrying PSG supporters.
Police did not indicate which group of fans launched the attack.
Olympique Lyonnais (Lyon) said in a statement it "condemns this violence" and later blamed "a clear error" in route planning.
"For reasons that are still not clear the police escort decided to pass seven Lyon buses in the middle of the 18 PSG coaches at the toll booth in Fresnes," the club said.
"And that was after all parties involved had been working for the past two months on separating the (traffic) flow.
"As a result of such an obvious route error violence erupted with its origin yet to be determined."
The statement noted that several Lyon fans had been injured by armed PSG supporters.
"The club encourages victims to take legal action from today so that light can be shed on these events."
The French Football Federation called the violence "unacceptable".
After the match in Lille, which PSG won 2-1, supporters left the stadium calmly, amid a heavy police presence.
Earlier, fans of the rival teams had mingled all day without incident ahead of the 9:00 pm (1900 GMT) start time.
The regional police authority said 1,000 officers were on duty in the town and a further 1,000 in the stadium.
The local authorities had also put in place a number of measures for the high-risk match.
Fans were forbidden to move "outside the areas reserved for them" near the stadium until 04:00 am Sunday, and authorities banned the public consumption of alcohol "in a glass or metal container" until the same time.
