The English translation sounds imperative. Should there not be some sort of imperative in French also?
No, because the French imperative form is not similar to the infinitive:
- Aie des frites (2nd person singular)
- Ayons des frites (1st person plural)
- Ayez des frites (2nd person plural)
by the way, we would not use verb "avoir" in that case, but "prendre":
- Prends des frites (2nd person singular)
- Prenons des frites (1st person plural)
- Prenez des frites (2nd person plural)
So statements like "Here, have some nuts." or "Take a couple of my beers." wouldn't be imperative statements in French?
Yes, indeed when you are faced with human beings.
However, "having fries" or "have fries" are often equivalent to "avoir des frites", in longer sentences, like "avoir des frites au déjeuner est fréquent dans les cantines scolaires" (having fries at lunch in school canteens is frequent).
Also note that the infinitive verb form also replaces imperative in writing in recipes and user manuals.