When parents are taking small children shopping where I live (Stoke-on-Trent), the phrase is "Going Tat- taahhs", which is not to be confused with going on a summer holiday, which is of course "Going Big Tat - taahhs".
Further to the above answer, "faire les/des courses" is not in the least colloquial, but is perfectly standard French. Although "courses" does also mean the races, both uses of the word come from the Italian "corsa" = "to run". There is therefore no particular link between shopping and horseracing; it's just that the Italian word has evolved to encompass a series of meanings in modern French.