Lyrically, the song uses the metaphor of Joan of Arc to explain that even strong people have fragile hearts and can break down, showing that the air of self-confidence that someone can carry through an entire life may be just a shield for insecurities.
The song received positive reviews from most music critics, who commended her raw vocals, the revelatory lyrics that matched with the album's thematic and noted it for being a highlight on the record.
[4] To avoid further leaks, Madonna released six completed tracks with the pre-order for the album on the iTunes Store on December 20, 2014, as an "early Christmas gift".
Gad was also responsible for programming, additional backing vocals and the song's instruments, which were also played by Afsheen, Cumbee, Stephen Kozmeniuk, Dan Warner (guitar) and Lee Levin.
[13] Lyrically, the confessional song talks plainly and plaintively about the detachment and loneliness that Madonna feels in the face of the press, with the singer lamenting: "Each time they write a hateful word / dragging my soul into the dirt / I wanna die.
[12] The chorus, which features skittering drums and strings, has Madonna simply saying: "I don't wanna talk about it right now / even hearts made out of steel can break down.
[...] More than any of the previously released songs, 'Joan of Arc' also establishes one of the foundational themes of Rebel Heart, albeit one not always evident when wading through the poorly sequenced album.
"[16] Ben Kelly of Attitude called it "a fresh sounding pop guitar tune treading new territory for her, and which could carry serious currency as a single,"[8] while Nick Levine of Time Out labeled it "a sublime electro-folk ballad.
"[10] Music critic Alexis Petridis wrote in The Guardian that the song is one of the "indispensable moments" on the album, "on which the singer genuinely seems to be revealing her personal feelings and frailties", saying that it is "cut from the same emotional cloth as Like a Prayer's 'Promise to Try' or Ray of Light's 'Drowned World/Substitute for Love'.
"[19] John Marrs of Gay Times agreed with the Like a Prayer-style influence, noting that "[v]ocally and lyrically she could easily be channeling Eva Peron, so don’t cry for her too much.
"[24] On the other hand, Consequence of Sound's Sasha Geffen had mixed feelings about the song, calling it a "lukewarm love [track that] couples easy, inoffensive melodies with historical Christian imagery.
Madonna was dressed in a sequined heart blouse,[32] with the performed track being "slightly slower than the studio version, while parts of the song [had a minimal production]".
[32] Digital Journal reviewer Markos Papadatos wrote that it was "an outstanding vocal performance", where Madonna "showcased tremendous control over her voice, and allows the lyrics to speak for themselves.
[36] Madonna also added the song to the set list of her Tears of a Clown free concert in Australia—an intimate show where the singer combined a mix of acoustic music, comedy and storytelling.