It's not so much August that has shut down most everything but rather Sunday. Pretty much everything is closed on this day, at least as far as shopping goes; some supermarkets may be open on Sundays, but they'll close around 12:00 or 12:30.
(There is actually a French law prohibiting Sunday openings unless it is for a "cultural" outlet such as cinemas, museums, theaters, etc.
I put quotes around the word cultural because around 15 years ago the Virgin superstore on the Champs Elysees decided to open on Sundays. They consulted their employees and there were enough who said they'd like the extra income to open the extra day.
The government told Virgin that they had to shut down on Sundays. Richard Branson (Virgin's owner) being Richard Branson, he opened the store the following Sunday. The government told him if he did that again there would be a fine imposed. The following Sunday he opened the store again. The government said that if he did that again, they'd close him down.
This situation became a national issue, inspiring the French newsweeklies to write cover stories on if French culture was threatened by Sunday openings.
Anyway, Richard Branson being Richard Branson, this question was taken up by the National Assembly, and a way was found to satisfy Branson—since the Virgin store sold books and records, it was a cultural outlet and so was allowed to open on Sundays.
Just a little story to give you some background on why practically everything is closed on Sundays.)