I cannot understand how the astonishing number of people I see wearing denim on summer weekends avoid heat stroke. The man on the left in the illustration does a good job of illustrating how to deal with the season.
Start as he does, with a linen short sleeved shirt, preferably one with cuffs on the sleeves and two pockets on the chest, and self-belted shorts made from cotton or linen. Consider tieing a cotton bandanna around the neck but don't worry about it either way. Slip into a pair of espadrilles, with or without ankle ties, and head for the bar for a cold drink like the French 75. Pour a jigger of gin into a flute, add half a glass of sparkling wine or champagne, lemon juice and simple syrup to taste, and top off with more sparkling wine. Add a straw hat before going out into the glare.
On cooler days or slightly more formal occasions, substitute linen trousers for the shorts. And that sums up summer casual. Don't forget the drink.