In medieval France, people may have smoked something, possibly opium or hashish or another cannabis derivative. There was a "Society of Smokers", sort of an artists collective. No one is sure, however, whether there was any actual physical smoking occurring, but since tobacco hadn't been introduced yet if there were, then it had to be an Old World substance.

We have record of this in songs from medieval France, specifically from the compositional school known as the Ars Subtilior, particularly the song "Fumeux Fume par Fumee" by Solage, about whom we know very little except that he composed many of the works in the Chantilly Codex. This particular rondeau is remarkable for its low tessitura (vocal range) and what was at the time (and for another three or four hundred years or so) extravagant chromaticism characteristic of the Ars Subtilior. Fumeux fume par fumee

edit: here is a better performance. If you don't do anything else today, listen to this piece of music. It really is remarkable.

The text (lyrics) for those wondering:

The smoker smokes through smoke, A smoky speculation. While others smoke in thought, The smoker smokes through smoke, Because smoke pleases him greatly As he meditates. The smoker smokes through smoke, A smoky speculation.

EDIT: To clarify, these are the lyrics to "Fumeux Fume par Fumee" by Solage. I meant to reply to (what is currently) the top comment by citrusonic about evidence of smoking in medieval France.

An add on question: in my literature class the other day we read Shakespeare In the Bush, and it mentioned the African tribesman knocking off coals from the fire and into their pipe, did they just smoke wood?

People have asked this question and similar questions about this in the past. Answers vary depending upon if the discussion is about northern Europe, the Mediterranean, the Middle East, or the Far East (e.g., China).

Herodotus claimed that the Scythians would smoke marijuana by sitting in a tent filled with smoke. Is there any truth to this claim?

Smoking in the Old World before Columbus

Before the introduction of tobacco to the Old World what did people smoke? note that OP asked about the Old World, but the top comment pertains strictly to Europe

Did people smoke in the Old World before the introduction of tobacco and, if so, what?

Smoking in Europe before the discovery of the New World

Was there a culture of smoking in Europe before the introduction of tobacco, opium, and marijuana?