Using lime wedges, moisten the rims of six glasses. Set limes aside for garnish. Sprinkle coarse sugar on a plate. Hold each glass upside down and dip rim into sugar. Set aside. Discard remaining sugar on plate.
In a blender, combine lemonade concentrate and raspberries; cover and process until smooth. Press mixture through a fine sieve; discard seeds. Return raspberry mixture to blender; add ice, strawberries, blueberries, 1 tablespoon sugar and tequila. Cover and process until smooth.
Pour into prepared glasses. Garnish with reserved limes.