Well, sort of a spin-off of an embryonic idea I had....
The French Revolution goes a bit more moderate, and though the Revolutionary fervor does result in several sister republics throughout the Mediterranean and Central Europe, the biggest change is that the Consulship and Empire are avoided. A more egalitarian and democratic spirit is born in the Western World.
This spreads to the New World as well. The Zeitgeist of Revolutionary France, which has stuck to ending Slavery infects Jeffersonian America and Slavery is outlawed in the West by one vote.
Without the bogeyman of Napoleon, discontent with the ruling class in the United Kingdom boils over and Great Britain and Ireland erupt in successful revolutions, ending the British Empire but increasing the forces of democracy in the world.
The relation between the European republics and peoples of Africa and Asia are gradually changing. The children of tribal chiefs and kings are brought on scholarships to Paris and Oxford to learn Western Enlightenment thoughts and ideals, which they take back to their homes.
Trade is more guided by laissez-faire and less by the idea of exclusive colonial trading partners. Several Afro-European joint partnerships are established to exploit the wealth of the continent. Profits from raw materials is reinvested in infrastructure and industry.
Though there is still racism, it is a much more subtle force and gradually fades as an anachronism. There are still wars, some terrible, but they are more between the upstart Republics and the last vestiges of the old, autocratic forces. Russia is one of the last to fall to Revolution.
By 2010, most of the world is united in a loose confederacy, with a very similar standard of living across the globe.
Vive le Revolution, Vive le Afrique!