All characters existed in real life, except John Falstaff. In Henry IV Parts 1 and 2, William Shakespeare based Falstaff loosely on the historical Sir John Oldcastle, a companion of Prince Henry. He renamed the character because of Oldcastle's powerful family.
The battle of Agincourt was filmed in two weeks, with 300 men and 80 horses, in a field in Hungary. To achieve a muddy battlefield, the crew would let horses run over it. The weather was so hot that the mud kept drying up in between takes, so they moved the battlefield to the left and did the same process again.
The scar on Henry's cheek is historically accurate. The real Henry V was struck in the face by an arrow at the battle of Shrewsbury in 1403, when he was 16 years old. In the movie, it's the scene in which Henry fights Percy Hotspur. The arrow was removed, but it left a permanent scar.
Timothée Chalamet stated that his funniest memory from filming was seeing Robert Pattinson vaping on set, in full armor and make-up.
The Dauphin's heavily French-accented English was intentional, to better insult and disrespect King Henry. David Michôd cast Robert Pattinson very early in the writing process because he needed the Dauphin to "pop out", stating "I love how bold Rob is, I wanted him to go nuts with it. His whole purpose is to be a jerk and to just torment Hal. So I kind of needed him to be a larger-than-life jerk. He needed to be ridiculous. I just knew that he would want to sink his teeth into this character and that he would make it fun."