During the ancient times, there was an city called Carthage. This place was originally founded by the Phoenicians. It was also once a major center of trade and influence. And the Carthaginians who dwell in this city fought for a couple of times already against the Roman Armies. But since Rome had the military strength to destroy many of their enemies, the Carthaginians also fell into the hands of the Romans. There was the Battle of Carthage and Punic Wars that occurred in human history.
Since the ancient Carthage was originally founded by the Phoenicians, it only means that the Carthaginians are also Phoenicians. As they were not strong enough to defeat the Romans probably because their military power was not strong, they fell into their enemies hands. The city of Carthage was completely destroyed during the Third Punic War. This was ended in 146 B.C. Wars usually took place in the ancient times because of political power and the desire to expand their territories. This was the same reason why Carthage and Rome had conflicts.
If you are curious about the language of the Carthaginians, it is the Punic language. From the first Punic War up to the third Punic War, the main and greatest reason why it took place is due to conflicts that started by the Carthaginians and it finally resulted to the Romans having control over many different cities within and around Rome. The Carthaginians attacked Rome and almost destroyed it. But in the end, it was Carthage that was destroyed.