In the first half of the XXth century, French and English were the main international languages.
During and immediately after the first congress in Paris, 1924, the French acronym for "Fédération Internationale des Echecs" was actually FIE, and it was referred in the English-speaking world as "International Chess Federation" or ICF. But already the following year, at the Congress in Zurich, French-speaking members (and possibly Italy) made a point that "fide" meant "trust" in Latin, thus the 'D' was added for the name to symbolize the confidence of its members in the institution, and FIDE became the official acronym in both languages (and worldwide).
E.Winter's Chess Notes have a very interesting article about the birth of FIDE:
‘FIDE was founded in 1924’ say the history books, yet, technically speaking, that could be disputed. Certainly the Fédération Internationale des Echecs was formed that year, but its Statutes systematically referred to it as ‘FIE’, and not ‘FIDE’:
But it doesn't give the reason of the later change:
But later in the year, for reasons as yet unclarified, ‘FIDE’ became the official acronym. If ‘FIDE’ appeared in print in 1924, we have yet to find it.
I remember reading that the Latin meaning was the motivation for switching to "FIDE" in some chess-history book in French, but I will have to dig further to source it properly.