Demande vs. requête
The French words demande and requête both translate to "request", but they differ significantly in their level of formality and specific use cases. While demande is the everyday, versatile term used in most situations, requête is much more formal and is often reserved for legal, technical, or highly official contexts.
Demande
The word demande is the most common and versatile term for a request or an application. It is used in everyday conversation, business, and administrative contexts to describe the general act of asking for something, such as a favor, information, or an official document.
Je vais faire une demande de passeport demain.
(I am going to make a passport request tomorrow.)
Le directeur a accepté ma demande de congé.
(The manager accepted my request for time off.)
C'est une demande tout à fait raisonnable.
(That is a completely reasonable request.)
Nous avons reçu de nombreuses demandes d'informations concernant ce produit.
(We have received many requests for information regarding this product.)
Il a complètement ignoré ma demande d'aide.
(He completely ignored my request for help.)
Requête
The word requête is a more formal or specialized term for a request, petition, or query. It is primarily used in legal proceedings to petition a judge, in computing to describe a data query made to a server, or in highly formal situations where someone is pleading for a specific action from an authority.
L'avocat a déposé une requête auprès du tribunal ce matin.
(The lawyer filed a request with the court this morning.)
Le serveur ne peut pas traiter cette requête informatique en raison d'une erreur.
(The server cannot process this computer request due to an error.)
Le roi a écouté la requête de ses sujets avec beaucoup d'attention.
(The king listened to the request of his subjects with great attention.)
Votre requête a bien été prise en compte par nos services administratifs.
(Your request has been duly noted by our administrative departments.)
La base de données a répondu à la requête en une fraction de seconde.
(The database responded to the request in a fraction of a second.)
Summary
In short, use demande for almost all standard, everyday, and general business requests. Reserve requête for legal petitions, computer network queries, or highly formal pleas to an authority. If you are ever unsure, demande is almost always the safe and natural choice in everyday French.