To best answer this fascinating speculative question, it is first useful to understand what territories comprised the French colonies in North America during the period of their greatest extent. In 1534, Jacques Cartier, while searching for a hypothetical trade route to Asia known as the Northwest Passage, discovered the St. Lawrence River in eastern Canada. He claimed the entire region for the king of France, calling it New France. In 1608, Samuel de Champlain founded Quebec. Other French colonists who were mainly concerned with the fur trade formed alliances with Native Americans in the area and explored westward and southward, where they discovered the Great Lakes, the Ohio River Valley, and, eventually, the Mississippi River. The French explorer La Salle claimed the entire Ohio River and Mississippi River Valleys for France. The French built a number of forts in eastern Canada, the Great Lakes area, and Louisiana. Their original intent was to construct a string of forts in a broad arc all the way from the St. Lawrence River to the Gulf of Mexico.
Now we can speculate as to what would have happened if France had kept its colonies in America. New France would have comprised all of eastern Canada, all the lands around the Great Lakes, and all the lands on either side of the Mississippi River from its source tributaries to the Gulf of Mexico. This would have locked the British colonies that later became the United States into a relatively narrow strip along the Atlantic coastline. When the Americans rebelled and formed their own country, there would have been no room for expansion. Instead, it is possible that the French would have explored and settled westward across the central portion of the United States, possibly even contending with the Spaniards for domination of the North American west coast region. The United States might have remained an insignificant power, while France's influence would have been enormous. This is just one possibility. Use your imagination to think of what else might have happened.