If one conjugates verbs and declines nouns, what is it called when an adjective is "conjugated," as it is in French to agree in gender and plurality with the noun? (E.g. "beau" is masculine singular and "belles" is feminine plural.)
When learning languages or simply more casually, the verb agree is often used. For example, beau agrees with the masculine singular noun Jean-Claude.– BladorthinTheGreyOct 25, 2016 at 22:49
As curiousdannii said, it's a type of inflection.
In Latin, adjectives were traditionally classified as nouns (nomina; specifically nomina adjectiva); the nouns that weren't adjectives were called "substantives" (nomina substantiva). Latin adjectives and substantives are very similar morphologically, so it makes sense to group them together when talking about inflection. So we say that a Latin adjective is "declined."
In some other languages, such as German, adjectives are morphologically more distinct from substantives than in Latin, but the terminology of "declension" is still used, probably due to the Latin tradition.
My impression is that the word "decline" is not used as often when discussing languages without case, such as English and French. However, it's not incorrect to say that a French adjective is declined for gender and plurality.
I am not sure how those things work in English, but in Portuguese we don't use "conjugar" or "declinar" like that; one does not usually conjugate a verb when using it in a flexed form in normal speech or writing. In this case, we rather use the substantive "concordância" and the related verb "concordar": "o verbo concorda em número e pessoa com o sujeito": "the verb agrees/concords/matches with the subject in number and person*". The whole phenomena are respectively called "concordância verbal" and "concordância nominal".
Conjugate is a verb which means specifically inflecting verbs, and decline for nouns, but neither of those words are needed when you can just say inflect and inflection.