The E2I initiative, Macron had unveiled during a speech on Europe in September 2017, shortly after taking power, aims to bring together European countries to collaborate on planning, carry out joint analyses of emerging crises and to react to them quickly.
For the first time since March 16, Yellow Vests were able to take their demands to the Champs-Elysees, an area to which they are banned since the scenes of violence experienced at the beginning of the year.
"Never, since the end of the second world war, has Europe been so important", the French president said.
The French armed forces minister, Florence Parly, said before the parade that the flyboard could "allow tests for different kinds of uses, for example as a flying logistical platform or, indeed, as an assault platform".
German Chancellor Angela Merkel was among the foreign leaders present for the event, while German, Spanish and British aircraft took part in the fly-past.
The former jetskiing champion and military reservist Franky Zapata clutched a rifle as he soared above the Champs-Élysées on his futuristic machine, which the French military has helped to develop.
Macron's speech was met by boos from some protesters who attended the ceremony Sunday.
On Sunday, television images showed police grabbing one of the movement's leaders, Eric Drouet, as he stood on the sidelines of the parade and escorting him away.
Macron hosted a lunch at the presidential Elysee Palace with the other European leaders.
Mr Macron's European Intervention Initiative is a 10-country coalition of European militaries ready to react to crises and the French-led initiative, which includes Germany, Belgium, Britain, Denmark, Estonia, the Netherlands, Spain and Portugal, was launched previous year. The French-led initiative, which includes Germany, Belgium, Britain, Denmark, Estonia, the Netherlands, Spain, and Portugal, was launched past year, according to Reuters.