is farmer a common noun or a proper noun

A farmer farmed

Farmer Jones farmed
See the difference?

Proper nouns have capital letters at the beginning.

town, village, city = common nouns

Des Moines, New York, Riverside = proper nouns

What will you decide?

is farmer a noun

"Farmer" is a common noun. A common noun is a general name for a person, place, thing, or idea. In this case, "farmer" is a general term used to refer to anyone who engages in farming. Proper nouns, on the other hand, are specific names for people, places, or things. For example, if we were talking about a specific farmer named John Smith, then "John Smith" would be a proper noun.

I suspect the questioner is asking whether Farmer Brown farms, or farmer Brown farms.

See the difference?
If the farmer Mr Brown is generally known as Farmer Brown, the word farmer has been elevated to a nominative category unique to Mr Brown and thus ascends the rank to be regarded as proper, categorically speaking; thus, you can happily apply a capital.