‘Trans people are sacred. We are divine.’ The first line of I, Joan at the Globe establishes the tone of the play as a public rally for non-binary folk. The writer, Charlie Josephine, seems wary of bringing divinity into the story too much, and he gives Joan a get-out clause to appease the agnostics.

‘Setting aside religiosity we’ll settle for more of a street god, a god for the queers and drunks… a god for the godless.’ What can ‘a god for the godless’ mean? No idea. Joan throws in a few more hipster platitudes about ‘elevating our humanity, finding the unity hidden inside community, remembering our collective connectivity fuels courageous creativity [sic]’. At press night these rhapsodic banalities were cheered so aggressively that one feared the consequences of not joining in, or of not honking loudly enough.

Act One traces Joan’s military successes as she leads the Dauphin’s army to Reims (or ‘rants’ as the actors pronounce it). In the second half, her battlefield skills desert her and she’s accused of witchcraft by 42 black-clad judges.

Historically the piece is accurate but the costumes and the moral tone are snugly rooted in today’s culture rather than in Joan’s. The medieval court has been designed like a skate park with a rear wall arranged as a wooden chute which the actors climb up and whoosh down comically. It’s funny the first six or seven times. Then it gets tiresome.

Joan’s rhetoric becomes a little grating as well. She shrieks that she’s ‘full of God’ rather too often, and she has a habit of complaining that the dictionary lacks the words to express her complex, subversive and multi-layered personality. But that’s true of us all. And it’s a peculiar complaint to hear from the central character in a three-hour play devoted to her unique story.

At the Dauphin’s court, she befriends a chap called Thomas who shares her anxieties about her identity and who offers her succour and encouragement. Which is very handy for her but it diminishes the intensity of her dramatic mission. Joan is a teenage prodigy who seeks to change the course of history in an era of warlords and knights. So why does she need a male accomplice to help her out? A solitary struggle would be more gripping.

The court is nominally ruled by the Dauphin, who lazes around in tennis whites and listens to bad advice from his prattling all-male cabinet. After his coronation, he strips down to a pair of M&S underpants. The point is to portray him as an emasculated halfwit but this malign characterisation is rescued by Jolyon Coy’s superbly languid comic performance. Some of his scenes are as funny as Blackadder. The Dauphin appears not to mind that his court has been taken over by women. His heavily pregnant wife, Marie, orders him to carry the train of her dress as she strides around glaring imperiously at terrified underlings.

Marie is herself dominated by her mother, Yolande (Debbie Korley), who wears a shrill blue power frock, like Mrs Thatcher. She revels in her triumphant femininity. ‘In this world of men,’ she declares, ‘if you want anything done well, hire a woman.’ The audience cheered that statement like a bunch of brainwashed Young Conservatives in the 1980s. To portray the court as a matriarchy is an amusing piece of mischief but it also mars the drama by weakening Joan’s rebellion against male authority. What’s the point of this yarn if women rule already?

The show’s best feature is the inventive music performed by three excellent percussionists in an upper gallery. But the grinding length of the script undermines its value as entertainment. How come no one at the Globe suggested editing a few speeches and trimming the repetitive dance routines? Too scared, perhaps.

Farine Clarke’s London Zoo looks at the dog-eat-dog world of newspaper publishing in the 1990s. The internet is causing news-stand sales to fall but one title, the Daily Word, has posted a rise in circulation. This makes it a target for bosses at the ruthless UK National News Group who want to buy the paper, boost its advertising income and bank the profits. This is an age-old dilemma. Should the readership or the advertisers govern a paper’s editorial direction? Traditional wisdom states that the readers are king but the yuppies at the news group want to defy that rule and make off with the loot.

We follow the journey of Arabella, a sensitive graduate who has to navigate the shark tank with the support of an amiable but weak accountant Charles. They’re opposed by the avaricious Christian, a self-adoring misogynist, who makes no secret of his amoral nature. Though set in the media world of the last century, the themes of manipulation and greed feel perfectly up to date.