In fact, Shakespeare's concern with historical accuracy is non-existent. Although the characters and events are based on things that actually happened, in the century before his birth, his sole purpose was to produce entertaining and dramatic action for the troupes of actors with whom he was associated; he had little interest in educating his audience. The sources on which Shakespeare drew for this period included the Chronicle of Raphael Holinshed, which was itself a literary as much as a scholarly work.
Warning: wikipedia contains spoilers
The play opens in the aftermath of the death of King Henry V of England (although it was written before Shakespeare's play, Henry V. News reaches England of military setbacks in France, and the scene shifts across the English Channel, to Orleans, where "La Pucelle" (Joan of Arc) is encouraging the Dauphin to resist. She defeats an English army led by Talbot (Sir John Talbot, 1st Earl of Shrewsbury).
While in France, Talbot and fellow Englishmen pluck roses in the garden of a countess, when Richard, Duke of York quarrels with him about his claim on the throne. The lords select red or white roses, depending on whether they favour the House of Lancaster or that of York. Edmund Mortimer, a leading claimant to the throne, is a prisoner in the Tower of London, and declares Richard his heir. The young Henry VI honours both Richard and Talbot. The latter dies bravely in his next battle against the French. In the meantime, King Henry is married off to a young French princess, Margaret of Anjou, who has been discovered by the Earl of Suffolk. Suffolk intends to dominate the king through Margaret. Ill feeling between him and the Duke of Gloucester continues to fester.
This is one of few occasions where Shakespeare allows the action to be left to drift somewhat at the end of the play, the action of which was to be continued in Henry VI, part 2