I can only speak for the French standardization, but here’s how it happened. It dates back to the 19th Century. It started in Bordeaux, where their main foreign clients were the English. But French & English never had the same measure system, so it was hard to find an agreement. The Imperial Gallon was up to 4,54609 “litres”. So they had to find an easier way to count. Example of a common ground: wine was put in barrels of 225 liters, or 50 gallons. 225 liters also equals 300 bottles of 75cl. 1 barrel = 50 gallons = 300 75cl bottles. It’s just a game of “find the common determinator”. Also, it explains why wine was (and still is) sold in boxes of 6 or 12. 6x0.75 =4.5 (1 gallon)
Source: Jean Marc Bahans ; Jean-Robert Pitte : La bouteille de vin, histoire d’une revolution, Tallandier 2013
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The shortest answer is because Title 27 of the Code of Federal Regulations, 1979, standardized "fills" for wine and liquor. One acceptable "fill" is 750mL.
§ 4.72 Metric standards of fill.
(a) Authorized standards of fill.
The standards of fill for wine are the following:
3 liters. 375 milliliters.
1.5 liters. 187 milliliters.
1 liter. 100 milliliters.
750 milliliters. 50 milliliters.
500 milliliters
(Forgive the formatting; the smaller measurements are in their own 'column' in the original. It's not 3 litres + 375 millilitres; it's 3L or 375mL).
And for liquor:
§ 5.47a Metric standards of fill (distilled spirits bottled after December 31, 1979).
(a) Authorized standards of fill.
The standards of fill for distilled spirits are the following:
(1) For containers other than cans described in paragraph (a)(2), of this section—
1.75 liters
1.00 liter
750 milliliters
500 milliliters (Authorized for bottling until June 30, 1989)
375 milliliters
200 milliliters
100 milliliters
50 milliliters
This was based roughly on the "fifth" (4/5ths of a quart of 1/5th of a gallon), "short quart", or "commercial quart" which had become somewhat popular. For a history of bottles, and how to date bottles (especially American bottles), please see here. For examples of 750mL-ish bottles, search the page for "fifth".
I cannot find any specific laws on European bottle sizes, but I do have an unsourced quote from Jean-Robert Pittee, author of a book on Bordeaux winemaking:
«0,75 litre est le douzième d’un double gallon anglais (une unité de mesure anglo-saxonne correspondant à 4,5 litres, ndlr). La contenance de 0,75 litre semble avoir été inventée à Bordeaux en vue du commerce du vin vers l’Angleterre en caisses de douze.»
(Please note, Googlers: I had to change the square brackets in this quote to parentheses because of Reddit's version of Markdown.)
Which, translated roughly, means:
0.75 L (750mL) is roughly 1/12th of an English double-gallon (4.5 litres). 0.75 litres seems to have been invented in Bordeaux for easier wine trade to England in cases of 12.
There is evidence for the double-gallon existing, at least for milk.
Basically: it's fairly similar to reasonably common pre-metric measurements in both England and the US for alcohol, and provides an option between half a litre (which itself became obsolete for liquor in the US as of 1989) and a full litre. People who imported alcohol into the United States now had a reasonably easy bottle size to create, which, assuming their home country did not have any laws against that size of bottle, could be used at home as well.
As a follow up question, when and why did the standard size for vodka in what is now Russia become 500ml?
This might suit Soviet era historians.