Tout de suite
At once, or right away, is the literal translation of this French phrase. This is very often written incorrectly as tout suite. The English have never been comfortable with adopting French terms into English and, compared with Latin phrases say, there aren't as many as we might expect considering how close the two countries are geographically. This ambivalence, and the fact that most English can't actually speak French or even make a decent stab at pronouncing French terms, is the source of the attempts to poke fun at the French by deliberately mispronouncing those French phrases that have made it into English - in this case as toot sweet. This teasing dates back to the First World War; for example:
Arthur Empey, in Over the top, 1917 - "'Toots Sweet.' Tommy's French for 'hurry up', 'look smart'.
Punch, 1917 - Tommy (to inquisitive French children): "Nah, then, alley toot sweet, an' the tooter the sweeter."
The 1968 film Chitty Chitty Bang Bang included a song call Toot Sweets. This led to the marketing of confectionery with the same name, in the form of sugar whistles.
The phrase excuse my French takes this a step further in implying that French is inherently linked with profanity. More recently, this phenomenon has been made fun of in the many comic mistranslations of French phrases put into the mouth of Del Boy (David Jason) in John Sullivan's comedy Only Fools and Horses; for example, mange tout - used by Del Boy to mean 'my pleasure' and creme de la menthe - 'the very best'.
See also - other French phrases in English.