People often conflate correlation and causation; Jansenism occurring at the same time as the Revolution does not mean it led to it; there were so many other factors to take into account in relation to the revolution, including the already strained classes, the Enlightenment ideals, and the cost of the American Revolution.
The doctrinal movement of Jansenism was a Christian theological movement was primarily in France. The people emphasized on original sin, human depravity, the necessity of divine grace, and predestination. The movement originated from the posthumously published work of the Dutch theologian Cornelius Jansen which died in 1638. It was first popularized by Jansen's friend and was led by Antoine Arnauld.
Jansenism, which was condemned by the Pope, emphasized original sin, divine grace and predestination. The main factors which led the French Revolution were poverty, taxes and the Enlightenment. France was essentially bankrupt and its poor lived in extreme poverty. The nobles lived very lavishly and the King kept raising taxes on the people to fund a series of wars as well as his excessive lifestyle. Combining those with Enlightenment principles on government led to the French Revolution, rather than Jansenism.
Extreme poverty in the working classes led to the French Revolution. Successive French kings bankrupted the nation and then the French people were inspired by the American Revolution. The aristocracy was clearly out of touch when Marie Antoinette intoned, "Let them eat cake" in response to starving people who had no bread. That phrase typified French anger at their leaders which caused drastic action to be taken against the ruling class.
No, I do not think the doctrinal movement of Jansenism led to the French Revolution, because there were other movements that were more popular at the time. The movement towards natural rights, spurred by John Locke and deToqueville had far more of an influence toward the French Revolution than Jansenism did.