I don't know about Carthage specifically, but Phoenicians are reported to have circumnavigated Africa. The relevant passage is Herodotus 4.42:

Libya is washed on all sides by the sea except where it joins Asia, as was first demonstrated, so far as our knowledge goes, by the Egyptian king Necho, who, after calling off the construction of the canal between the Nile and the Arabian gulf, sent out a fleet manned by a Phoenician crew with orders to sail west about and return to Egypt and the Mediterranean by way of the Straits of Gibraltar. The Phoenicians sailed from the Arabian gulf into the southern ocean, and every autumn put in at some convenient spot on the Libyan coast, sowed a patch of ground, and waited for next year's harvest. Then, having got in their grain, they put to sea again, and after two full years rounded the Pillars of Heracles in the course of the third, and returned to Egypt. These men made a statement which I do not myself believe, though others may, to the effect that as they sailed on a westerly course round the southern end of Libya, they had the sun on their right - to northward of them. This is how Libya was first discovered by sea.

The passage I marked in bold is the key. That could only have been said by someone used to the sun in the southern part of the sky who had crossed the equator. It is ironic that the statement Herodotus rejects is the one that proves the story true. Whether it was Phoenicians or not, someone crossed the equator, observed the movement of the sun, and returned to Europe or else Herodotus could never disbelieve the story.

EDIT for clarity: Talking about the equator was short hand. I should have referred to the tropics as you can be below the Tropic of Cancer and above the equator. Stupid tilted orbit.