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Ciel vs. firmament

While both ciel and firmament can be translated as sky in English, they are not interchangeable. Ciel is the common, everyday word, whereas firmament is a more literary, poetic, and specific term.

Ciel

A1
The word ciel is the standard, most frequently used term for sky. It refers to the atmosphere above the Earth, the weather conditions, and can also mean heaven in a religious or figurative context. It is an extremely versatile word used in daily conversation.
Le ciel est bleu et sans nuages aujourd'hui.
(The sky is blue and cloudless today.)
L'avion volait très haut dans le ciel.
(The plane was flying very high in the sky.)
Le ciel est menaçant, je crois qu'il va pleuvoir.
(The sky looks threatening, I think it's going to rain.)
Quand elle a appris la nouvelle, elle était au septième ciel.
(When she heard the news, she was in seventh heaven.)
Il a prié le ciel pour que tout se passe bien.
(He prayed to heaven for everything to go well.)
J'adore regarder les couleurs du ciel au coucher du soleil.
(I love to watch the colors of the sky at sunset.)

Firmament

C1
The word firmament is a sophisticated and literary term that specifically refers to the vault of the heavens, especially at night, perceived as a vast dome studded with celestial bodies. It evokes a sense of grandeur and is often used in poetic, astronomical, or biblical contexts.
Des milliers d'étoiles scintillaient dans le firmament.
(Thousands of stars were twinkling in the firmament.)
L'astronome utilise un télescope pour observer les objets lointains du firmament.
(The astronomer uses a telescope to observe distant objects in the firmament.)
Le poète décrivait la beauté du firmament étoilé.
(The poet was describing the beauty of the starry firmament.)
Cette actrice est une nouvelle étoile au firmament du cinéma.
(This actress is a new star in the firmament of cinema.)
La Voie lactée traverse le firmament d'un bout à l'autre.
(The Milky Way crosses the firmament from one end to the other.)
Le silence de la nuit n'était troublé que par la lumière des astres dans le firmament.
(The silence of the night was only disturbed by the light of the stars in the firmament.)

Summary

In essence, use ciel for all general, everyday references to the sky, weather, or heaven. Use firmament when you want to be more poetic or formal, specifically referring to the vast, star-filled celestial vault at night or in a figurative sense for a group of luminaries.