The English word “belief” can refer to religious faith, personal conviction, an opinion, or the acceptance that something is true. The correct French translation depends heavily on the specific context and the strength of the conviction being described. There is no single one-to-one equivalent.

Croyance
This is the most direct translation for “belief,” particularly when it involves faith, religion, or something accepted as true without absolute proof. It often relates to ideas that are not empirically verifiable.

• Il faut respecter les croyances de chacun.
  We must respect everyone’s beliefs.
• La croyance en un dieu unique est fondamentale dans cette religion.
  The belief in a single god is fundamental in this religion.
• Cette vieille croyance n’a plus cours aujourd’hui.
  That old belief is no longer held today.

Conviction
This word denotes a strong, deeply held belief or principle. It implies a firmness and certainty that often guides a person’s actions. It is stronger than a simple opinion.

• Il agit selon ses convictions politiques.
  He acts according to his political beliefs.
• Elle a la conviction profonde que la justice prévaudra.
  She has a deep-seated belief that justice will prevail.
• Je respecte votre conviction, mais je ne la partage pas.
  I respect your belief, but I do not share it.

Foi
This term is used almost exclusively for religious faith or a powerful, trusting belief in something intangible.

• Elle a une foi inébranlable.
  She has an unshakable belief/faith.
• Il a perdu la foi en l’humanité.
  He lost his belief in humanity.
• La foi peut déplacer des montagnes.
  Belief can move mountains.

Idée
In some contexts, “belief” can be translated as idée when it refers to a notion or an opinion that someone holds.

• Se faire une idée.
  To form a belief.
• J’ai dans l’idée qu’il va accepter.
  I have a belief that he will accept.

Opinion
When “belief” is synonymous with a personal view or judgment, opinion is an appropriate translation.

• Chacun a le droit d’avoir ses propres opinions.
  Everyone has the right to their own beliefs.
• C’est mon opinion personnelle.
  It is my personal belief.

Le fait de croire
Sometimes, especially when referring to the act or state of believing, a verbal construction is the most natural choice.

• Le simple fait de croire en quelque chose peut avoir un effet.
  The simple belief in something can have an effect.

Special cases and set phrases

• To the best of my belief.
  À ma connaissance.
• Beyond belief.
  Incroyable.
• It is my firm belief.
  Je suis fermement convaincu que…

Summary

Use croyance for beliefs involving faith or acceptance without proof. Use conviction for strong, guiding principles. Use foi for religious faith or a powerful trust. Use opinion or idée for personal views. The context determines the most accurate word.