Something quite interesting I've learned researching the French Revolution is, like Vietnam and Iraq of the modern era, the event was quite popular in America in the beginning, but lost mass appeal only after things started going so terribly wrong. Given France greatly helped America achieve victory over Great Britain in the Revolutionary War, most (but not all) American patriots initially supported the French Revolution. Most Founding-era Americans viewed this historical event done in the name of "liberty, equality, and fraternity," as an extension of American Revolutionary principles. Most commentary that explains the meaningful differences between the American and French Revolutions, why the former succeeded and the latter failed, was written after the fact. Those who supported the American cause but opposed the French from the beginning, like Edmund Burke, were a minority then, but whom today we herald for their predictive wisdom.
The spirit of the age (the "zeitgeist," if you will) of the American and French Revolution was Enlightenment -- liberty, equality, rationalism, the rights of man, hatred of political tyranny and confidence in man's reason were the enlightenment ideals in which both American and French Revolutionaries fervently believed. On religious matters, Enlightenment led many to reject Christian orthodoxy for deistic or unitarian rationalism. However, many remained true to Christian orthodoxy while simultaneously embracing Enlightenment ideals. These republican Enlightenment ideals, I would stress, are, for the most part, not authentically biblical concepts even if orthodox Christians promoted them or the Bible was used to advance such ideas.
First, the Bible is not at all a political revolutionary book. Jesus (or his disciples like Paul) did not abolish one social or political institution. Not tyrannical government, not chattel slavery, not rule of Kings, not one. Today social liberals who preach the "social gospels" I believe misuse the Bible as do the Christian Marxists who advanced "liberation" theology. However, American Whigs who used the Bible in revolt against Great Britain were just as guilty of advancing something the Bible does not support: the right to political revolution. Be it the American or French (or quite frankly any political) Revolutions, Marxist governments or a modern social welfare state, none of these notions is "biblical." And all who would use the Bible in support of such are equally guilty of misusing the good book.
The Ancient Israelites had a theocracy, not a republic as one Whig preacher inaptly posited. Many of these political sermons reproduced by the Liberty Fund, as fascinating as they are to read, are about as hermeneutically sound as biblical arguments in favor of same-sex marriage.
What should bring this point home is many of these same theologians who argued on behalf of the American Revolution from the pulpit -- some orthodox Christians, some theistic or unitarian rationalists who rejected Christian orthodoxy -- likewise used similar arguments to support the French Revolution. The most notable aphorism of the pro-revolutionary theology of that era was "rebellion to tyrants is obedience to God." Now, this sounds nice, and as a liberty loving, tyrant hating classical liberal, this is the kind of God in which I would like to believe. However, this notion -- like America's Declaration of Independence -- is hardly biblical. Theistic yes, biblical no.
A great article by Gary B. Nash, which you probably can't access without paying $9 unless at a library or educational institution with license privileges, details exactly what I've noted above: the plethora of "patriotic American preachers," some orthodox Christians, some not, who supported the French Revolution, at least at the beginning and saw "the project" as a continuation of the American Revolution. The follow page that I've reproduced discusses Ezra Stiles, President of Yale, one of the most notable patriotic Whig preachers, who was both an orthodox Christian and an Enlightenment rationalist who originally supported the French Revolution and saw its ideals as a continuation of the American Revolution.