The American Revolution was a model for the French one. If it fails there will be profound effects in France and all of Europe. There is likely to still be a revolt in 1789 as all the causes are still in place; but with no republic in America to draw inspiration from it may be very different.
No Tennis Court Oath.
No Declaration of the Rights of Man.
No insistence on tearing down the monarchy completely.
Instead we might see the estates general aiming at reforming the monarchy on the British model. Louis the XVI is forced to abdicate for some other more liberal King. France is stripped of its absolutism with the nobility and the Estates General. Europe is shocked but is not horrified. England especially looks on at the more liberal French monarchy with approval.
With this the Terror, the Napoleonic Wars, and the spread of democratic ideas through Europe disappear. The needs of the peasant class and the poor have not been addressed. This may lead to trouble in the future but not in the eighteenth century.
The American Revolution was not the only influence on the French Revolution. Most of the factors are in fact internal. And the first two years of the revolution were in fact a parliamentary monarchy. It was only the fault of Louis XVI personnality that he was deposed and executed. If the revolution in the US is crushed, there will be two things : the moderate won't have a great leader (as Lafayette won't be as popular), and if the subsequent repression by the british is very harsh, the english parliamentary model (which was probably the most important influence in the early revolution) will be discredited.
Also the revolution will happen latter, probably after another war in which the French Crown need to borrow money, as new taxes won't be needed and the
Etats Généraux thus won't be called by the King.
The early parliamentary monarchy won't be as friendly to the king, and there will be probably more true republicans as opposed to those favorable to an english-like system.
All of the influence of the French Revolution are here : The Declaration of Independance, the Enlightment Philosophers and the various english declarations. So, the
Serment du jeu de Paume would probably happen even if in another form or name, it was basically the first act of the revolution. The
Déclaration des Droits de l'Homme would happen too, all the "preliminary work" was done. And as i said before, more influence to tear down the monarchy as the revolution will be more radical, due to the lack of influence of the moderate, and thus Louis XVI will make a mistake earlier, which will lead to the First Republic.
Louis XVI will never abdicate. He never did IOTL, and he was just too conservative to do it. If the more radicals revolutionnary have an earlier influence we could see some things different than IOTL (like Robespierre proposal to abolish the death sentence).
In America once all the rebel leaders have been executed the British would definitely have modified their rule there and granted the colonists limited autonomy. Perhaps even an early Dominion status. The British would have ruled over Canada and the eastern half of North America.
If history teach us anything, is that the british aren't really the type to soften after crushing a rebellion. The repression will probably be harsh, and the concept of colonial self-rule will be thrown back by several years.
With no United States and no Manifest Destiny expansion into the interior, never mind to the Pacific, would have been greatly slowed. The Indian tribes would have prospered, Mexico would have held onto Texas, California, and its other possessions. Russian Alaska would also be a fixture of this new world.
The Indian Tribes won't prosper under the british rule and american outlaw settlers. Russia would probably sell Alaska to the UK and what happen to Mexico depend on how the things unravel in Europe.