Below is my more glib analysis:
[America is] a democracy and a republic. Revolutionary France called itself a republic. France also recognized a "higher law" -- a theism to undergird its principles to which they appealed; they simply -- like America -- re-envisioned this monotheistic God to be more "revolutionary." And this is one reason why many American Christians at the time supported the French Revolution and saw it as a continuation of the American.Okay, so first Barton claimed the difference between revolutionary America and France is that America was founded to be a "republic," France a "democracy."
This is false. The terms "democracy" and "republic" accurately describe both founding era America and revolutionary France. The terms are not mutually exclusive. And yes, America's Constitution promises each state a "republican" form of government. Revolutionary France, likewise termed itself a "republic." (That is they didn't say, "we are a democracy, not a republic.")
(For more on why America is both a "democracy" and a "republic" see Eugene Volokh's post here.)
Second, Barton intimates a feature that distinguishes democracy and republic is that democracy is "the will of the people," republic is "higher law" (which Barton apparently conflates with his understanding of "the Bible").
I think a kernel of truth lies underneath Barton's confusion. Democracy, in its rawest sense, does mean "majority rule," at its worst "mob rule," something arguably more present in the French Revolution than the American. Both the late 18th Century American and French systems sought to pay due respect to "the will of the people." And both believed in limits on such. Small r "republican" checks on the "democratic, majoritarian" process. Such "republicanism" means certain structures are built into the system that operate as as check on raw democratic majoritarian rule.
And those "checks" don't necessarily have anything to do with "higher law." Rather they are things like the checks and balances built into the American constitutional structure, the separation of powers, and the fact that it's elected representatives as opposed to "the people" themselves who write the statutes. The people elect the representatives to "do their will." And most of the time, hopefully, the "will" of both converge.
But not always. When "the people" are subject to fanatical passions, America's founders hoped the will of the more elite refined elected representatives would temper those passions.
Barton's misrepresentations relate more to the nature of unalienable rights. The "liberal" qualifier in the concept of "liberal democracy." If we were a pure "direct democracy," then majority would always win. But that's not our system. Rather, majority wins sometimes, most times in fact. But not always. Certain rights are antecedent to majority rule. Those are the small l "liberal" rights with which a small d "democracy" must deal.
That's one "republican" check on the democratic process, among many, in the kind of "democratic-republic" that both America and France in the late 18th Century were founded to be.
There is no easy answer for determining, in politics, which principles the majority gets to "win on" and which principles are antecedent to majority rule. Harry V. Jaffa termed this dilemma the "Crisis of the House Divided."
("All men are created equal" + the rational truth that blacks are "men," that is "mankind" or human beings = slavery has got to go; but the Constitution makes compromises with the institution of slavery. The Declaration + Constitution put together = an anti-slavery Founding and Lincoln securing a promise America's Founders made but could not or did not keep.)
One way in which to "settle" the issue as to which rights are "liberal"-- that is, antecedent to majority rule -- is tie them to God. This is what Barton intimates distinguishes the American Founding from the French Revolution.
But revolutionary France too tied their liberal rights to God. In fact, all three of France's "Declaration of the Rights of Man, like America's "Declaration of Independence" appealed to a generic deity as the ultimate guarantor of liberal rights, antecedent to majority rule.
This should surprise not as America's Declaration of Independence greatly inspired the French Revolution and its author, Thomas Jefferson, went to France and assisted in the writing of their Declaration of the Rights of Man, fomenting the French Revolution.
Barton seemingly intimates the theistic "higher law" that undergirds liberal rights in America's system is, unlike that of the French Revolution, from the God of the Bible. But America's Declaration of Independence doesn't claim this. Instead, it appeals to a God in four places [1. Natures' God; 2. Creator; 3. Divine Providence; 4. Supreme Judge of the World] without ever explicitly identifying such God as the Christian one, or quoting verses and chapter of Scripture. The revolutionary French documents do more or less the same appealing to the generically defined "Supreme Being."
During the Founding era, the term "nature" especially as it relates to religion means discovered by reason as opposed to revealed by God in sacred scripture. As it were, the phrase "laws of nature and of nature's God" is a double invocation of reason. Yes, I would say, America's Founders like the French Revolutionaries believed in a higher law as ascertainable by reason.
Christians, yes, after thinkers like Thomas Aquinas believe in such and make "reason and revelation," properly understood work together. And the principles of the French Revolution are compatible with such. This is why so many Christians of apparent orthodoxy like Ezra Stiles supported the French Revolution and saw it as a continuation of the American.