How did hidden government expenditures cause debt in France?

I'm going to try and answer this question assuming you mean government expenditures that incurred debt in late 18th century France, an important cause of the fall of the ancien regime and the beginning of the Revolution.
It was problems of debt incurred in fighting the Seven Years' War and in supporting the American Revolution that led to the eventual downfall of the Bourbon monarchy. The crown's debt had already grown as a result of excessive and ostentatious spending on the part of Louis XV, but the situation became even more dire under Louis XVI. His ministers instituted radical reforms and taxation schemes that angered the aristocracy. Some of these tax levies were blocked by the noble parlements, who in asserting their influence and challenging the tendency to absolutism argued the king didn't have the right to make these decisions without consultation.
The king was eventually forced to convene the Assembly of Notables in 1787, and they were shocked at the debt levels of the French crown. This financial crisis eventually forced the king to assemble the Estates-General for the first time in over a hundred years in order to legitimize his desire to levy new taxes. The convening of this body, which became radicalized as the first National Assembly, led to the Revolution and the eventual overthrow of the monarchy.