Has civilization accomplished the goals that our Founding Fathers and French Revolutionaries sought to achieve when they drafted documents such as the Declaration of Independence and the Declaration of the Rights of the Man and of the Citizen, respectively?

Any question involving the complexities of history over a 240 year period cannot have a simple yes or no answer. But in this particular case, I would have to say that my answer would tip the scale more on the affirmative than the negative side.
The primary documents of both the American and French Revolutions stressed the goal of equality among men and the right of men to determine how they should be governed. In 1789, virtually all the countries of Europe, with a handful of notable exceptions such as Switzerland and the still-independent Venetian Republic, were monarchies. And in all monarchies, except (ironically so, given the American rebellion) Great Britain, the sovereign had a degree of power and a lack of accountability to the people as a whole, or even to the upper classes, that we would find unacceptable today. The establishment in North America of a large, independent Republic was seen in Europe as an experiment that would probably fail, even by those who had been sympathetic to the American cause. For instance, Edmund Burke, who, like others in the Whig Party, had been against the war to suppress the rebellion, did not even mention the new United States in his Reflections on the Revolution in France (1790), in his effort to show that the French Revolution could not succeed and that traditional forms of government—in other words, monarchies—were the only ones that could succeed in a country the size of France or any of the major European states at the time.
With the Reign of Terror, and with Revolutionary France becoming a dictatorship under the Directory and then under Napoleon, Burke's predictions seemed at first to be borne out. In the settlement at the Congress of Vienna after Bonaparte's final defeat in 1815, the victorious powers did all they could to turn back the clock and restore the status quo ante bellum as it had been in 1792. But certain things had changed that could not be negated by the Powers. In their invasion of the German and the Italian states, the French had introduced in those countries positive changes in the legal systems which remained permanent, even after the French were expelled. In addition, Bonaparte's troops had abolished the ghettos in which the Jewish population had been confined, and discriminatory laws against Jewish people began gradually to be abolished. The ideals of equality articulated in the Declaration of Independence and the Declaration of the Rights of Man and of the Citizen had been absorbed into the European mindset and created irrevocable changes in the thinking of not only European intellectuals but the population as a whole. Serfdom was abolished in the states where it existed, even, finally, in Russia in 1861. Similarly, as imperfect was the application of those ideals in the newly formed United States, the attempt in 1861-65 to break up the Union through secession and war failed, and the enslaved people were emancipated, though the establishment of Jim Crow laws after the Civil War meant that they had to wait another hundred years for real liberation to occur. But it has occurred, despite the flaws in society that have continued in the form of institutionalized racism.
Both in Europe and the United States, changes promoting true equality among people were introduced gradually. Great Britain, though it had been the closest already to having a democratic government, gradually expanded its voting laws to include the population as a whole, while the sovereign's power decreased to the point where eventually he or she became a figurehead as head of state, while real power resided more and more completely in Parliament. The countries on the Continent lagged behind in similar processes, but eventually, if we fast forward to the mid-twentieth-century after the two World Wars were over, all the countries of Western Europe became democracies. The emancipation of women, their being granted the right to vote and to enter the workplace in professional jobs and in large numbers, occurred somewhat earlier but were part of the same overall process of liberalization and democratization.
But this progress has been limited, of course, to only certain parts of the world—the Unites States, Canada, Australia, Western Europe, and only some countries in Latin America, the Middle East, Africa, and Asia. The overthrow of communism in the Soviet Union did not, ultimately, result in democracy, and China, despite being a society in which economic free enterprise thrives, is still an authoritarian state. So much of the world does conform to the ideals expressed in those founding documents, imperfectly so, but in a way that is a vast advance over the state in which the world found itself in the eighteenth-century. Whether our democratic institutions will be maintained and will be accepted, as well, by those countries on the "outside" now, no one, of course, can know for sure.