A contingent of French infantry in India for joint military exercises led the march down the capital's central Rajpath avenue, the first time foreign forces have ever taken part in the parade.
Indian Prime Minister Narendra Modi invited Hollande as chief guest in a show of solidarity with France after Islamist attacks in Paris last November killed 130 -- recalling a 2008 assault on Mumbai that killed 166.
The two leaders agreed in talks Monday to deepen cooperation on counter-terrorism in the wake of the Paris attacks and a deadly siege this month on an Indian air force base near the Pakistan border.
The mood on Tuesday was more celebratory, with Modi -- sporting a gold turban that rivalled the spectacular military headgear on display -- and Hollande chatting as they sat side by side in a bulletproof glass enclosure.
An estimated 10,000 spectators braved thick smog and air quality levels classified as hazardous on the US embassy website to watch the display.
Delhi is the world's most polluted capital and levels of PM2.5 -- the tiny particles that can enter the bloodstream -- frequently reach 10 times the World Health Organization's safe limit.
But the skies remained dry, unlike last year when chief guest US President Barack Obama was forced to shelter under an umbrella throughout.
Human pyramid
The mounted camels of the Border Security Force -- an annual highlight -- put in an early showing, decorated in brightly coloured caparisons.
A dog squad drawn from the Army's Remount Veterinary Corps returned to the parade after a gap of 26 years to perform a march past wearing striped coats in their unit's colours.
They were followed by motobike stunt riders perforning a human pyramid, another annual tradition.
India launched a nationwide security crackdown in the lead-up to the celebrations, making a string of arrests. Some 50,000 police, army and paramilitary forces were deployed across the capital on Tuesday.
The parade, which also features colourful floats showcasing the culture of the country's states, is the highlight of annual celebrations of the birth of modern India.
It marks the adoption of the country's constitution on January 26, 1950 following independence from Britain in 1947.
It was the fifth time a French president has been chief guest, the biggest honour India can bestow on a foreign leader.
Later Tuesday Hollande will meet the head of the opposition Congress party Sonia Gandhi before ending a three-day official visit that began in the northern city of Chandigarh.
His visit had raised hopes of a conclusion to a long-delayed, multi-billion-dollar deal for New Delhi to buy 36 French Rafale jet fighters.
But the two sides said they had not yet arrived at an agreement on the price, which experts say could reach around five billion euros ($5.6 billion).
