What was the need to call the Estates-General of 1789?

The reason for the meeting was finance. I don't have that research to hand, but France was absolutely screwed for finance. They had a structural deficit and had tried everything (including inventing entirely new and fantastic monetary systems, firing successive finance ministers, etc.) There wasn't a mechanism to levy new taxes or to change the allocation of existing taxes. It had been tried, and internal inertia and hostile stakeholders had ruined the effort (Imagine that every bureaucrat in France was Ted Cruz).

update in response to comments. The King could declare a new tax, but unless he went door to door to collect it, he would receive no tax revenue. Tax collectors performed the function their fathers did, in the way their fathers did, and distributed the revenue the way their fathers did. The tax collector didn't work for an institution, he held a sinecure, and there was no real way to remove him from office. (which had something to do with the levels of corruptions which are unimaginable to modern students.) Every tax collector, every judge, every magistrate, every gendarme, every minor elected official had their own version of how the government was supposed to work. (actually they had two - one they paid lip service to, and one they actually carried out day to day.) If the King declared "Water is wet", the entrenched bureaucracy of these street level bureaucrats would interpret that as "The King has declared that water is wet, and in accordance with my ancient prerogatives and the authority of my office, I interpret that to mean that I should have more jam on my bread!". And there wasn't anyone in the whole country that could disagree. The king could dismiss you from his presence, and might be able to dismiss you from a top level office, but he didn't control enough offices in the country to make a difference. It was "personal rule" not just because he ruled without governance, but because the limit of his authority was the limit of his personal influence.

There is an excellent source (I've lost the title and reference, but the paper made a deep impression on me) about efforts to reform the French Salt Tax. Can anyone recall?

France didn't have the equivalent of a constitution, or a real legislative branch. France had a perplexing combination of absolute personal rule combined with entrenched customs that could not be altered by any known mechanism.

If I remember correctly, the Estates General was called as a "Hail Mary" play - get the largest possible buy in to the emergency measures necessary to keep the country from disintegrating into anarchy.

Additional resources provided by the redoubtable @LangLangC

• France and the Failure to Modernize Macroeconomic Institutions provides a bit more context for the assertions I've made above - two quick examples:

  Further complicating matters was the ability of regions, groups and individuals to obtain tax exemptions. Over time, this patchwork quilt of taxation produced a sense of general inequity in the tax burden and resistance to the imposition of new taxes or reduction in tax privileges. The ability of the Crown to gain new taxation was hindered by the absence of a national representative institution that could grant new taxes legitimacy. Furthermore, the tax collection system was operated by contractors who had considerable autonomy.

and

The ceremony of enregistrement was required to legitimize a monarch’s edicts, making them enforceable at law throughout the kingdom.

Which is a tightly packed clue to the failure of governance that created the need to summon the Estates General.

• Revolution and State Structure: The Bureaucratization of Tax Administration in Early Modern England and France This one is locked behind a registration wall, and is therefore unlike to be the resource I recall.