Formel vs. soutenu
While English uses the word "formal" to cover a wide range of situations, French makes a clear distinction between formel and soutenu. generally, formel relates to following official rules, protocols, or being explicit, whereas soutenu refers specifically to an elevated or sophisticated level of language and vocabulary.
Formel
B1The word formel describes something that adheres to strict conventions, official procedures, or etiquette. It focuses on the exterior form or validity of an action. It is also used to describe something categorical or beyond doubt.
Les relations entre les deux collègues sont restées très formelles.
(The relationship between the two colleagues remained very formal.)
Nous devons suivre une procédure formelle pour déposer une plainte.
(We must follow a formal procedure to file a complaint.)
Il m'a donné l'interdiction formelle d'entrer dans son bureau.
(He gave me a strict prohibition to enter his office.)
Pour cette soirée, une tenue formelle est exigée.
(For this evening event, formal attire is required.)
C'est une promesse formelle que je ne briserai pas.
(It is a solemn promise that I will not break.)
Soutenu
B2The word soutenu is used almost exclusively in linguistics to describe a "high register" of language. It refers to speech or writing that is sophisticated, literary, refined, and grammatically complex. It is the opposite of familier (casual/slang).
Dans un registre soutenu, on ne dit pas sympa mais plutôt agréable.
(In a formal register, one does not say nice but rather pleasant.)
Le professeur demande aux étudiants d'utiliser un vocabulaire soutenu dans leurs dissertations.
(The professor asks students to use elevated vocabulary in their essays.)
Ce roman est écrit dans un style très soutenu et difficile à traduire.
(This novel is written in a very sophisticated style and is difficult to translate.)
Lors de son discours, le président a adopté un ton grave et soutenu.
(During his speech, the president adopted a grave and formal tone.)
L'inversion du sujet est une marque du langage soutenu.
(Subject inversion is a mark of formal language.)
Summary
Use formel when discussing official rules, strict protocols, dress codes, or explicit guarantees. Use soutenu strictly when discussing language style, grammar, or vocabulary that is elegant and refined.