Comparison with Marlborough is questionable. He was an aristocrat and Bonaparte was not, to put it mildly. In the late XVII - early XVIII there were never-ending European wars. With Louis XVI alive and everything else being the same, which wars with French participation are you talking about? Wars between Austria and Prussia were pretty much over and their best effort was pathetic “Potato war” in which France did not take a part.Let's say Louis XVI is a more asserive and proactive monarch who clamps down on the excess privilege of the first two estates, all the while garnering a base of support by appealing to the salons as well as those who wish for a more Prussian style military structure. As a result, serious question over the status of the Bourbons remains unknown until the mid-nineteenth century when it has to face the industrialization efforts of the British and the Prussians. In the meantime, how does one Corsican soldier advance along an army rising in discipline and advanced military strategy?
Given Bonaparte will still have his ambition and his genius I can see him having a similar path as the Duke of Marlborough: fighting numerous campaigns on the European mainland, ecspecially across the German spheres of influence being contested between Austria and Prussia, while on the domestic front he becomes known for switching alliances based on what will gain him influence in the court and the Estates General as well as revolutionizing warfare away from Marlborough's fields of attacks towards styles that took in the increasing power of cannons.
Promotion in the French army of that time was, IIRC, mostly by a seniority and would be broken only to favor the aristocrats. So, unless you turn Louis XVI into somebody completely different and somehow fix the French finances, France is not going to fight any wars for a number of the decades to follow and the only chance for an ambitious officer with no social connections and money is to look for the employment elsewhere. And there were only two places with the realistic chances for the career: Ottoman Empire and Russian Empire. IIRC, Bonaparte was considering the 1st and he did try the 2nd but could not agree with a recruiting agent regarding the conditions (did not want to have his rank lowered and the agent did not have a crystal ball to see the future). Can’t tell about the OE but in Russia with its frequent wars a chance for the promotion definitely existed.