The same way privileges for the nobility came about in all different kinds of societies

From Hippolyte Taine's The Origins of Contemporary France: The ancient regime

"In this epoch of perpetual warfare only one regime is suitable, that of a body of men confronting the enemy, and such is the feudal system; we can judge this trait alone of the perils which it wards off, and of the service which it enjoins...Every taste, every sentiment is subordinated to military service...

Thanks to these braves, the peasant enjoys protection. He is no longer slaughtered, no longer to be led captive with his family, in herds, with his neck in a pitchfork. He ventures to plough and to sow, and to rely upon his crops; in case of danger he knows that he can find an asylum for himself, and for his grain and cattle, in the circle of palisades at the base of the fortress. By degrees necessity establishes a tacit contract between the military chieftain of the donjon and the early settlers of the open country, and this becomes a recognized custom. They work for him, cultivate his ground, do his carting, pay him quittances, so much for house, so much per head for cattle, so much to inherit or to sell; he is compelled to support his troop.....

When we clearly represent to ourselves the condition of humanity in those days, we can comprehend how men readily accepted the most obnoxious of feudal rights, even that of droit du seigneur. The risks to which they were daily subject were much worse.

Taine, 7-8

In the years before the revolution there were attempts to change the taxation and spending system of the French state. In large part the French State was broke from massive spending on various wars like the American War of independence (2 billion livres), the lack of taxation on the wealthy and church like you mentioned, and the fact the French state had no budget (Hazan, 38)

"It was accepted that the king should spend as he saw fit, and that receipts were subsequently adjusted to this." (Hazan, Id)

Even before the Revolution there was an attempt to make the nobility and church pay taxes. It was apparent France's 4.5 billion livre debt was a real problem. But change was difficult pre-Revolution since the privileged don't like to give up their privileges.

In August 1786 Charles Alexander de Calonne, the controller-general, proposed a financial "revolution". It was a plan for a "territorial subvention", a tax on land that would be applied to all properties including noble, ecclesiastical, and common. Internal duties on products like grain which were paid by merchants and peasants would also be suspended. But the plan was never implemented because the "assembly of notables" convened in February 1787 turned down Calonne's request to change the system.

Hazan, 39-40

Sources: Hippolyte Taine The Origins of Contemporary France: The ancient regime Holt, 1876

Eric Hazan, A People's History of the French Revolution Verso, 2017