The original printed title of the play is: The History of Henry the Fourth; with the Battle at Shrewsbury between the King and Lord Henry Percy, surnamed Henry Hotspur of the North, with the humorous conceits of Sir John Falstaff.
As for many of the English histories, Shakespeare’s sources for The First Part of Henry the Fourth look like the usual suspects:
Raphael Holinshed’s Chronicles of England, Scotland and Ireland–Holinshed was only one of a three main authors of the work (the other two being William Harrison and Richard Stanyhurst), and their work was first printed in 1577.
Edward Hall’s The Union of the Two Illustrious Families of Lancaster and York
Samuel Daniel’s The First Four Books of the Civil Wars Between the Two Houses of Lancaster and York
A Mirror for Magistrates