The French Parlements, although etymologically the same as Parliament, were not the same politically. They were local courts and legislatures, more similar to the English shire system than to Parliament. In the US system, they most closely resemble state governments, although that's a very tenuous comparison. Regardless, the King repeatedly tried to reform taxation and was repeatedly blocked by these local governments. This was a problem as France was undergoing fiscal and social crisis at the time, and taxes would alleviate both.

None of the Parlements told him to call the Estates-General. The King, frustrated by the failure to implement his reforms, called the Assembly of Notables. This was a separate body, where the King appointed a bunch of people from all over the place to advise him. But he got to appoint them, so he could skew things in his favor. He asked them for a constitutional way to implement his reforms (with the unspoken understanding this meant getting the Parlements to comply or getting around them).

Perhaps he was hoping they would endorse his tax plan and give him the political capital to force it on them. Maybe he was hoping they would consider themselves to have the authority to modify how local government functioned. Maybe he was hoping he would create a bunch of political allies by giving them this honor, since many of them sat in local Parlements. They would then push it through Parlement. This is not entirely clear, because various people all argued for each of these outcomes. Maybe it was all of them.

What is clear is that it didn't work. The Assembly of Notables advised the King that the only way to force something on the Parlements was the Estates-General. It was the Estates-General that was most politically similar to the English Parliament. The Estates-General had not been called in a long time but it remained a constitutionally relevant entity. The King had to respect the constitution, in that there were institutions other than the King with rights and privileges. But the Estates-General, with the King, was virtually omnipotent. (As was English Parliament when the King assented.) They could have levied any taxes they pleased. They could have taken any other measures to alleviate the crisis as well.

But that's the issue: they're omnipotent and could take any other measures. And when the King's approval isn't forthcoming, they can start to pressure him to do things he doesn't want to. We know the French King was acutely aware that the strengthened 17th century Parliament in England had led to civil war, the death of Charles I, the dethroning of James II, the end of the Stuart dynasty, and reduced the King of England to a much less powerful person. The Royal Ministry feared reform that would (eventually) lead to either constitutional monarchy or, in the worst case, revolt and the death of the King.

But the social and fiscal crisis was so acute the King decided to do it anyway. And... well, the doomsayers were right, in the end.