There was a fairly substantial debate over the proper title for the head executive under the United States Constitution, even after the ratification of the Constitution which uses the title "President" in Article 2. Kathleen Bartoloni-Tuazon's For Fear of An Elective King is the most robust consideration of this I am aware of (and really the only consideration), but what can be seen from the Congressional record and the letters reveal that the term "president" was a very contentious term that went beyond merely a matter of etiquette or diplomatic norms.

Prior to the adoption of the United States Constitution, there was some precedent for using the term but it was not typically viewed as an executive. Many state governments during the colonial period had a "president," some of which maintained the position post-statehood (though largely these roles have been replaced with "governor"), but it was also strongly associated with the head of a smaller legislative body: the Continental Congress adopted the term "president," somewhat taking after the British use of "Lord President" for the leader of the Privy Council, and it was fairly typical that states with bicameral legislatures had a "Speaker" for the lower chamber and a "President" for the upper chamber (as was and is the case for the United States House and Senate). It was, at least initially, viewed as simply one who "presided" over a body and directed it without the connotation it would later carry of executive power.

In a sense I would say your question is (partially) wrong, because it was not really the "Founding Fathers" as would commonly be thought of who decided on the appellation "President" for the holder of the office. The office itself was titled "President of the United States," but there were many suggestions for what to actually call the "President" besides "President." Washington was, at his inauguration, called only "President of the United States," but there had been a proposal a week prior by Richard Henry Lee to have Congress consider and decide on the official title. Vice President John Adams put together a committee and made the first proposal suggesting "His Highness, President of the United States and Protector of their Liberties" to be the official title of the office with "His Highness" used as the shorthand. Adams would later suggest, though neither the Senate nor his committee gave much support, to instead using "His Majesty." A second faction advocated for a less regal title, but still a formal title, preferring either "Electoral Highness" or just "Excellency," which Adams (and Lee) rejected as it would, in their eyes, "demote" the President to no higher than "functionaries from German princedoms" or even that of colonial/state administrators (Pennsylvania, for example, referred to its chief executive as "President" until 1790). But this was somewhat in line with Washington's prior public image: as General Washington, he was typically styled and called "His Excellency" in public affairs.

But ultimately the House faction led by James Madison won out, calling him only "Mr. President" officially. There was a genuine concern for the Senate factions that an "informal" title like Mr President would deny the office respect both internationally and domestically and risk instead powerful groups being identified as the effective state. But the House (and a fairly large deal of the American public) did not want the trappings of a monarchy or the monarchical obsession with titles and desired the executive to function differently than a king. John Adams during this period was often called "His Rotundity" as a deliberate mockery of his proposed regal titles (and Bartoloni argues this "title controversy" did large and lasting damage to Adams politically). It should also be noted here that the official title was not President but rather Mr President: that Mr was a very intentional and meaningful inclusion during this period, as the title of "Mr" (as opposed to other titles, associated with nobility) was viewed as a more egalitarian and universal title. Bartoloni documented in her For Fear of an Elective King that a large swath of the American public started adopting the title "Mr" as it denoted nothing more than being a landowner and thus was not as strictly hereditary as the titles of nobility. Calling Washington Mr President thus was an intentional choice to reject monarchical tendencies and firmly establish a republican tradition within the United States.

Some sources if you are curious further:
Kathleen Bartoloni-Luazon For Fear of an Elective Monarchy
James Hutson "John Adams' Title Campaign"
Gordon Wood Revolutionary Character (see pages 50 - 54 in particular for the title controversy)