The word you use to translate "chair" and "purple" can depend on the specific kind of chair and purple you are talking about.
For a generic kind, you say "la chaise est violette".
"Pourpre" as a coulour would translate to "crimson", even though it's etymologically related to the English word "purple". "Mauve" is a specific shade of pale purple.
The generic word for "purple" in French is "violet" (feminine "violette").
The English word "chair" can have different translations in French. Depending on the kind, it would be "un siège" (something you sit on), "une chaise" (a chair with a back and no arm rest) "un fauteuil" (a chair with a back and arm rest) or even "une chaire" (a pulpit or a distinguished professorship at a university).
By default, without context, the English word "chair" is generally translated to "chaise".