Correct me if I'm wrong, but it seems to me that nobody much has a good word to say about Henry VI and it gets dismissed as bardic juvenilia quite a bit (I even remember Neil Gaiman having a go at the words "bad revolting stars" in Sandman at some point, and if Neil Gaiman considers himself safe to mock something else as hackwork then chances are it must be pretty bad).
Which is a shame because I really like this energetic 15th century Game of Thrones. With Henry V having recently popped his clogs the power balance of England and France are up for grabs and we are quickly introduced to a wide array of chancers, most of whom think they might do very well out of the impending chaos, thank you very much.
Boy-king Henry VI is endearingly sweet and wide-eyed (it's great how every Shakespearean monarch seems to be diametrically different in character to the last, creating a Doctor-Who-regeneration-like sea change in the flavor of proceedings after each coronation) but the biggest personalities in Part I are the cocksure Joan of Arc and the fierce but unfortunately dwarfish Talbot, neither of whom (spoiler warning) are going to be around for Part 2.
The vainglorious Frenchies are too big for their ridiculously ornate britches and it's easy to imagine how much fun the contemporary audience must have had booing - and cheering when the inevitable comeuppance arrives. The young playwright also has enormous fun with basically every male character acting like a teenage boy in the presence of an attractive woman. The scene for Part 2 gets set by the introduction of the hilarious Suffolk whose spontaneous hots for Margaret of Anjou engenders a Machiavellian plan to set her up with Henry so he can spend more time with her (he himself being unfortunate enough to be married to another, a fact he only remembers about 5 minutes into the scene).
Yes it's largely people running backwards and forwards on the battlefields of France, variously celebrating victory or bewailing misfortune, but it's all done with brio and humor and larger-than-life characters, so what's there to complain about? En route a pair of noble factions fall out while swearing to wear either a red rose or a white, clearly foreshadowing some pretty major plotlines in coming seasons.
Most poignant scene is the piteous fall from grace (perhaps literally?) of Joan "La Pucelle", gone from holy invulnerability to grovelling in the dirt before Richard of York, just a grubby French peasant-whore receiving scant mercy from her English captors. As in the Greek tragedies it's hard to know whether the audience would have had any sympathy for a foreign woman with ideas so far above her station, but for modern audiences, seeing a shining dream die so cruelly and abjectly is tough to watch.