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Comédie musicale vs. musical

While both terms refer to a production combining songs, spoken dialogue, acting, and dance, comédie musicale is the standard lexical term in French. In contrast, musical is a modern Anglicism increasingly used to emphasize a specific Broadway or West End style of production.

Comédie musicale

A2
This is the traditional and generic French term used to describe the entire genre. It applies equally to classic Hollywood films (like Singin in the Rain') and theater productions. It is the safest and most natural choice for everyday conversation.
J'ai acheté deux billets pour aller voir une comédie musicale ce soir.
(I bought two tickets to go see a musical tonight.)
West Side Story est probablement sa comédie musicale préférée.
(West Side Story is probably her favorite musical.)
Il n'aime pas trop le théâtre, mais il adore la comédie musicale.
(He generally doesn't like theater, but he loves musicals.)
Cette comédie musicale française a fait une tournée dans toute l'Europe.
(This French musical toured all over Europe.)

Musical

C1
Borrowed directly from English, this noun is used primarily by purists, critics, and marketing teams in major cities like Paris. It distinguishes authentic, Anglo-Saxon style productions (often sung through or with high production value) from the broader, sometimes looser definition of comédie musicale. using musical implies a trendy or professional appreciation of the specific art form.
Le Théâtre du Châtelet présente un nouveau musical de Broadway chaque année.
(The Théâtre du Châtelet presents a new Broadway musical every year.)
C'est un véritable musical qui respecte tous les codes du genre.
(It is a true musical that respects all the codes of the genre.)
Les critiques disent que ce musical est la révélation de la saison.
(Critics say that this musical is the revelation of the season.)
Ils ont décidé de monter un musical en version originale.
(They decided to stage a musical in the original version.)

Summary

Use comédie musicale in 95% of situations, as it covers movies, plays, and adaptations without ambiguity. Use musical specifically when discussing current theatrical trends, Broadway imports, or when speaking with industry enthusiasts who differentiate between the general genre and the specific Anglo-American art form.