The statement that best analyzes how Enlightenment ideas influenced the political structure and balance of power in Europe is:
Enlightenment ideas became the foundation for France’s first representative government.
This statement reflects how Enlightenment philosophies, which emphasized reason, individual rights, and the concept of government by consent, directly influenced the establishment of a representative government in France, particularly during the period of the French Revolution. This shift in governance also in turn impacted the political landscape across Europe.