It comes after last year's events were scaled back because of virus fears.
France's government decided to go ahead with the parade as part of a broader effort to return to pre-pandemic activity.
The number of onlookers were limited and they were restricted to a small section of the parade.
Each person attending had to show a special pass proving they had been fully vaccinated, had recently recovered from the virus or a had negative virus test.
Similar restrictions will be in place for those gathering to watch an elaborate fireworks show at the Eiffel Tower on Wednesday evening.
Spectators converged on Paris from around France, even if they were frustrated with the restrictions and long lines for virus security checks.
"I came especially for my son who is marching today," said Gaelle Henry from Normandy. "It's nice to be able to get out a little bit and finally get some fresh air and think that all the people are here, and that we are getting back to normal a little bit."
Masks were worn everywhere among the smaller-than-usual crowds along the avenue.
The marching soldiers were unmasked — the French military said they have all been fully vaccinated or freshly tested for the virus.
Last year's parade was cancelled and replaced by a static ceremony honoring health care workers who died fighting Covid. France has lost more than 111,000 lives overall to the pandemic.
Bastille Day marked the milestone of storming the Bastille prison in eastern Paris on July 14, 1789, commemorated as the birth of the French Revolution.