The battle on October 25, 1415 saw a heavily-outnumbered English army inflict a catastrophic defeat on the enemy that altered the course of the Hundred Years' War.
Commemorative services, Shakespeare performances, anniversary dinners, exhibitions, conferences and archery tournaments are marking the anniversary.
"By defeating the French, Henry V united the English. He was the last great warrior king of the Middle Ages," said Andrew Gimson, author of "Brief Lives of the Monarchs since 1066".
King Henry was 28 at the time of the battle, two years into his nine-year reign.
He is buried in London at Westminster Abbey, which is holding a service marking the anniversary on Thursday, six centuries on from the day when news of the victory reached the city.
The abbey holds king Henry's "funerary achievements" -- the personal items carried at his funeral, namely his sword, shield, saddle and helmet.
King Henry's sword will be paraded through the abbey once again on Thursday and placed on the altar.
Agincourt was immortalised in William Shakespeare's 1599 play "Henry V", whose stirring battle speeches still resound and feature in popular lexicon, including "Once more unto the breach, dear friends", "we happy few, we band of brothers", and "Cry 'God for Harry, England, and Saint George!'"
The Royal Shakespeare Company is staging the play at its base in the bard's hometown of Stratford-upon-Avon, central England, with Alex Hassell in the title role.
"Henry says that he and his troops shall be remembered because of their actions on St Crispin's Day until the ending of the world," Hassell told AFP.
"Well, we may not be there yet but being part of their remembrance 600 years on feels rather wondrous."
He added: "There will be an added weight to the notion of dying in battle, of legacy, of being remembered, and of making history".
Casualty estimates vary widely, but English losses are thought to have numbered more than 100, while the French lost thousands, including around 40 percent of the French nobility on some counts.
London guilds helped victory
The historic Worshipful Company of Bowyers, or bowmakers, held a special Agincourt Dinner on Thursday and hailed the longbowmen who it described as "a key component in a stunning victory".
The guild is part of the City of London, the British capital's financial hub, which is keen to recall its part in bankrolling the expedition.
It contributed 10,000 marks -- £3 million ($4.6 million, 4.1 million euros) in today's money.
It is putting on show the rarely-seen Crystal Sceptre, the 17-inch (43-centimetre) long mace given to the City by king Henry to mark his gratitude.
"Over the last six centuries, only a handful of people have seen or touched the Crystal Sceptre," the City said.
It is only removed from the Guildhall vaults for coronations and the ceremonial swearing-in of City of London mayors, who silently place their hands on it.
It contains red spinels from Afghanistan, blue sapphires from Sri Lanka and pearls from the Gulf.
"The story of Henry V is part of our national consciousness," said Guildhall gallery curator Katty Pearce.
The Guildhall exhibition also contains an iron mace used in the battle.
The anniversary is, of course, also being remembered in Azincourt, the village in northeastern France where the two armies clashed.
A remembrance ceremony will take place on the battlefield, involving French and British troops.