Languages that have some degree of inflection are synthetic languages. They can be highly inflected (such as Georgian or Kichwa), moderately inflected (such as Russian or Latin), weakly inflected (such as English), but not uninflected (such as Chinese).

Fusional languages or inflected languages are a type of synthetic language, distinguished from agglutinative languages by their tendency to use single inflectional morphemes to denote multiple grammatical, syntactic, or semantic features.

WALS has a very useful chapter and accompanying map based on maximally inflected verb forms (see links below). Have a look at how they define inflection to make sure that it overlaps with what you had in mind!

Inflected Languages: Inflection is a prominent feature in inflected languages, where words change to convey grammatical meaning. Latin, Russian, and German are examples of inflected languages. Examples of Inflections: Verb Inflection (Tense): walk (present) / walked (past) / will walk (future) Noun Inflection (Plurality): cat (singular) / cats ...

Unlike analytic languages, synthetic languages employ inflection or agglutination to express syntactic relationships. Agglutinative languages combine one or more morphemes into one word. The distinguishing feature of these languages is that each morpheme is individually identifiable as a meaningful unit even after combining into a word.