While I cannot speak for Bono, the general gist is that the American revolutionaries were using ideas from the Enlightenment which had a strong French component. One of the major influences in the structuring of American democracy was Montesquieu's De l'esprit des loix which articulated the ideas of separation and balance of powers, written constitutions, and republican government as hallmarks of a idealized society. Most of the Founding Fathers would have also been familiar with the works of the French philosophes like Voltaire or Rousseau.

But it would be too far to claim that the American Revolution was a wholesale French import. Montesquieu may have been an important intellectual on both sides of the Atlantic, but he was far from the only one. There were a large number of Enlightenment thinkers from the British Isles such as John Locke who also had an impact on the British American milieu. There also was a home-grown American Enlightenment as well with writers like Benjamin Franklin or Thomas Paine producing a number of works on the importance of liberty and government based on reason.