The most important thing for Carcassonne is flat comfy shoes for walking the old streets and walls, and a hat that shades your face!
Total generalisation but it generally works for any summer city trip: yes it’s hot but don’t dress like you’re going to the beach. So shorts would be more tailored than loose sporty styles, etc.
My standard suitcase suggestions would be:
Shorts x 2
T shirts x 3
short sleeve loose shirt x 1
dress x 2
Swimwear x 2
sun hat x 1
Flat sandals x 1
Trainers / comfy flat shoes x 1
cross body bag x 1
pants, bra, socks, etc
Pack with a complementary colour scheme and aim to have everything go with at least 2 other items. I usually go for navy, beige, cream or brown, and try and add colour via bag or sunglasses.
Oh, and have a look at Wears My Money for actual items if you need to buy stuff. She’s a blogger with some good thematic posts - Wears My Money. Also, I know she gets a lot of hate but Goop is usually worth a look for Euro holiday style ideas.
(This is all assuming that you are not going to be saddled with an enormous backpack full of sunscreen and kids stuff)