Why/how did the French Empire decline in North America?

In answering the question, it is good to have a standard for “empire” to compare. The standard for success is the British. There are many reasons the French were not as successful as their British counterparts in establishing a stable colony in America. Two reasons are especially important in understanding why the French were unable to sustain their colonization in America. Although some may argue the sale of the territories in the Louisiana Purchase was a great deal for the French!
The first reason is the French tended to settle further inland than other settlers. Transporting goods across uncharted and rough terrain made exporting the raw materials difficult. The French differed from the British in that the British were more interested in trading agricultural related products whereas the French were more involved in products like fur trading or essential mercantile items. The French were very good at developing mercantile type businesses that relied on settlers and indigenous people as their customer base rather than export back to Europe. By nature, the types of economic activities the French engaged were small in scale and independently owned. French traders did not rely on large investors to fund their operations like many in the British colonies. Investors expected a profitable return on their investment, and this required a stable financial and economic system which could only be accomplished by an established colony. Locating on the eastern coast and having to appease investors was a significant difference in the permanent settlement and desire to retain an interest in America by the British. The French did not have the financial investment in America to sustain their desire to maintain a colonial presence.
The second reason and most plausible is during the earliest times of exploration, and up to the late 1700s, the French were deeply involved in numerous expensive wars in Europe. When the French were not at war with a European neighbor, they were at civil war or revolution within the political boundaries of their own country. Wars and revolution took its toll on France and the French just were unable to sustain an interest in a continent thousands of miles away. The financial burden of wars in Europe and internally were too costly for the French to make a serious effort to colonize and maintain a significant presence in America.
Give the French credit. Though the French were unable to sustain a colony like the British, France sold the United States approximately 827,000 square miles of land west of the Mississippi River for fifteen million dollars. Though the French presence declined, the French still profited from their exploration.