"Joan of Arc" met with a positive critical response. Lenny Juviski of
The Northern Echo wrote, "Haunting and melodic modernists [OMD] with their best offering since '
Enola Gay'. Set to be a smash." In
the Face, journalist Ian Cranna felt the "lush, melodic" song had "obvious" hit potential; Cranna also ranked it no. 1 in a 26 November list of his "current listening pleasure". Sunie Fletcher of
Record Mirror said the track has a "tender mood" and is "not particularly striking on first hearing", but allowed that it may be a "grower" akin to previous single "
Souvenir". In a retrospective review,
AllMusic's Ned Raggett described "Joan of Arc" as "a towering heartbreaker, with Andy McCluskey and band in full flight". Critic
Dave Thompson observed a "revelation of a single" with a "gorgeous melody", adding that "the power of this song is almost equal to
Joan's own".
Trouser Press called the track a "magnificent, ethereal hit". "Joan of Arc" has appeared in various "best songs" lists, including musician and journalist
Paul Roland's "100 Essential Singles".
The Charlatans vocalist
Tim Burgess wrote, "For anyone who wasn't around in 1981 you could not go anywhere without hearing this song... such a classic." Former
Built to Spill bassist,
Brett Nelson, named the "melancholy and beautiful" track as one of the seven "milestones to [his] wanting to be a musician". ==B-side==