Violet and Purple are treated as distinct colours in the English language. However, I have learned that in French “violet” is the umbrella term for both purple and violet. Is this true? Also, what is the colour “pourpre” then?
In more technical areas of color discussion, what is "purple" in English (i.e. everything between indigo and magenta on the color wheel) is divided between "pourpre" on the reddish side of things (Pourpre being originally what English refers to specifically as Tyrian purple) and "violet" on the bluish side of things. (cf. Trésor de la langue française s.v. Pourpre & Violet, French Wikipedia...)
In the common language, however, pourpre has in practice evolved toward just being a general elevated/poetic synonym of violet (which now is roughly synonymous with English purple), because the specific shades of color that pourpre originally referred to are nowadays more likely to be referred to with wine-related words such as bordeaux or lie-de-vin.