Just the facts:

Carbon Definition & Meaning - Merriam-Webster

The word carbon comes from the Latin, carbo/carbonem (coal, charcoal), to the French, carbone, and in the 18th century to English.  Borrowed from the French word carbone, which was coined by the French scientist Antoine Lavoisier from the Latin.  In fact, in 1772 Lavoisier proved that diamond was a form of carbon, just like coal. 

The first English use of the verb carbon, according to the OED, was in 1922 in the Daily Mail (London). 

In German the word in Kohlenstoff, which literally means "coal-stuff". 

Strictly speaking, almost anything can be "organic" as long as it contains carbon, oxygen, hydrogen and nitrogen. The whole of organic chemistry is these four atoms arranged in different numbers and structures.