First, it's crucial to understand that the first Punic War, which Rome ultimately won, led to the two that followed. Rome would not have expanded into the western Mediterranean if it had lost the first Punic War to Carthage. Sicily would most likely be a part of Carthage, whose fleet would be one of the strongest in the Mediterranean. If Rome did not take back the captured cities, it would lose the ensuing Punic War, which would ultimately result in the total conquest of Rome by Hannibal's Italian expedition. The important thing to note is that the Mediterranean region and Europe would have a profound difference, especially in the past culture. It is worth noting that Romans were best known for their potential to conquer a region, incorporate it into their empire and expand on every good idea. The political system of Romans was very flexible, absorbing and benefiting the ruling classes. Romans also had a building passion than Carthagians, who did not possess the same attributes. For example, they did not have passion for construction, and if they were successful at war, their empire could not have endured to the establishment of the stable civilization base that was achieved by the Romans. Therefore, had Carthage won Punic War, the majority of the currently known government would be non-existence. Europe would not be the way it is today. There would be no main roads of Europe that the Romans made from England to the east of the empire. Had it won the Punic Wars, Carthage would with no doubt have become the most powerful in the Mediterranean, but it would not have expanded. As such, it would not have increased contacts with many other great powers.
Bibliography
Bagnall, Nigel. The Punic wars: Rome, Carthage, and the struggle for the Mediterranean. Macmillan, 2005.