Read the full text of Henry VI Part 1 Act 4 Scene 4 with a side-by-side translation HERE.
Imagine the scene: Talbot is swinging his sword in slow motion, fending off the French who are swarming around him, dodging arrows, all of that. Then suddenly his son arrives. Talbot tells his son that he called him here to teach him arts of war, so that Talbot's courage can live on in his son. But now, Talbot says, his son will die if he stays, and the Talbot line will be cut off. He tells the boy to take his swiftest horse and fly the scene.
John Talbot, the son, is having none of it. "Is my name Talbot? And am I your son? And shall I fly?" (4.4.13) Yep, Hollywood would be all over this dialogue. Talbot and his son debate the point, Talbot telling John to flee so that he can revenge his father and John insisting that someone who would fly in these circumstances would never come back for revenge.
John says that he'll stay, and his father can flee. But of course the older Talbot doesn't agree to this plan. They debate it, each trying to save the other's life, until finally they decide to fight side by side until they die. This is definitely the scene where the music would surge and the camera would pan out for a long zoom showing the grim battlefield and the hopeless odds and the Talbots side by side on white horses.
The French nobles rush in at this point and surround John Talbot, but his father swoops in to the rescue, shouting "Saint George and victory!" (4.6.1)
The Talbots really are all they're cracked up to be: bold, loyal, courageous, and strong. So the audience is likely to enjoy it when Talbot gives a speech about his son's courage and his rescue effort. He again asks if his son would like to flee so that he can avenge Talbot later, now that John has proven his courage.
John Talbot says in no uncertain terms that he's ashamed even by the suggestion that he would flee, and that he will stay and die with his father if that's what it takes.
Talbot accepts his son's decision and says they will fight side by side until they die, full of pride.
More fighting ensues.
Talbot starts to talk again, saying that young Talbot rescued him from the French, his son being "like a hungry lion" (4.7.7). Sounds pretty fierce.
Talbot describes how his son then leapt into the French, ferociously attacking them, and there died. Talbot is immensely proud of his son.
Soldiers enter, carrying John Talbot, who is actually not yet dead, but is dying.
Talbot celebrates the fact that he and John will escape death together today by entering immortality. This was a standard idea in the Renaissance, since belief in the Christian idea of resurrection after death was widespread. (John Donne talked about the idea in his poem "Death Be Not Proud").
Talbot takes his son in his arms and dies, celebrating courage and valor as he does.
The French nobles and Joan turn up.
Charles says that if York and Somerset had gotten their act together, it would have been hard on the French. This just underlines what a tragedy it is from the English perspective that the two couldn't cooperate: They might have saved the Talbots and won the battle.
The Bastard says that Talbot's son was raging and spilt a lot of French blood.
Joan says she tried to fight him, but he refused her as being unworthy to fight and went off to attack the other French forces.
Burgundy says that John Talbot would undoubtedly have made a noble knight.
The Bastard wants to chop the Talbots to pieces, which seems like a pretty brash insult, but Charles says they should show more respect to the dead bodies of those who made them flee in life.
Sir William Lucy comes in, wanting to know who has won, who the prisoners are, and who has been killed.
Lucy is especially looking for Talbot. Here he lists all of Talbot's titles, which takes upward of ten lines (4.4.172-183). They just go on, including a bunch we haven't even heard before in the play: Earl of Washford, Waterford and Valence; Lord Talbot of Goodrig and Urchinfield; Lord Strange of Blackmere; Lord Verdon of Alton, and more.
Joan says this is a silly way of putting it, and then goes on to call Lucy's style "tedious" and say that the person Lucy gives all these titles lies "stinking and flyblown…here at our feet" (4.7.78). Joan's very brave, but she could work on the chivalry a bit.
Lucy cries out in grief. He wishes that his eyes would turn into bullets so he could shoot the French, and that even the picture of Talbot would be a stumbling block to the French. He asks for the bodies of the Talbots and says he'll give them the burial they deserve.
Joan says they should definitely give Lucy the bodies—you know, because otherwise they will stink up the air. Again, you can tell that certain kinds of chivalry aren't her thing.
Charles gives the bodies to Lucy, who says that from their ashes will rise a phoenix to terrify the French.
Charles heads off to Paris, hopeful that he'll win everything now that Talbot isn't standing in the way.