The thoroughfare was reopened to traffic after the parade finished but a few hundred protesters from the grassroots "yellow vests" movement then tried to occupy it.
France's BFM television showed images of police firing tear gas to disperse the protesters, who tried to block the road with metal barricades, dustbins and other debris.
Several loud bangs could be heard. Protesters hurled objects at the police, booed and set a bin on fire.
The Paris Police Department said 175 people had been arrested since the morning and calm returned to the Champs-Elysees by 4pm.
Two prominent members of the movement, Jerome Rodrigues and Maxime Nicolle, were both detained by the police, according to AFP.
The Police Prefecture said on Twitter it had ordered the protesters to leave the area, or be forcibly removed.
Weekly demonstrations by yellow vest protesters have dwindled in size to just a few hundred people in recent weeks from about 300,000 nationwide in November.
As Paris authorities had banned all "yellow vest" demonstrations near the parade, many protesters did not wear the high-visibility jackets that give their movement its name.
Flags from the 10 countries of the European Intervention Initiative, a joint military pact created last year, led Sunday’s parade in Paris.
Alongside more than 4000 armed forces and more than 100 aircraft, the parade also saw a “flying soldier” as French inventor Franky Zapata soared through the air on his so-called Flyboard.
In a Bastille Day message published before the parade, Mr Macron said he wanted to highlight France's commitment to European security.
"Never since the end of the Second World War has Europe been so necessary. The construction of a Europe of defence, in connection with the Atlantic Alliance ... is a priority for France. It is the theme of this parade," Mr Macron said.
"Acting together and strengthening our ability to act collectively is one of the challenges that the European Intervention Initiative, along with other key European projects, wants to address," he added.
Although the clashes between protesters and police came after the parade, Mr Macron was audibly booed as he rode down the Champs-Elysées earlier in the day.
The French president and his guests had already left for the Elysées presidential palace for lunch before the demonstrations turned violent.
Agencies contributed to this report
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