If it is visit Paris, sit at and outdoor cafe and see the Louvre. Yeah, kids don't mess with your vacation except perhaps cost.
If you want to go to raves until 5 in the morning, do drugs and drink. Yeah, kids are a no no to take.
Then there is the in-between, which depends a lot on the type of kid and activity. One week surfing big waves somewhere, maybe possible if your kid has interest and are other smaller waves around. Impossible (or at least non recommended) if kid is afraid of the water and doesn't know how to swim. etc.
You can always take them, give them an ipad and let them spend 7 days in front of it, but at that point, why take them?
I am divorced but have a kid. Vacations (travelling) are usually split in two (or three). One week with my kid at someplace that is mostly for him (beachs + waterparks + etc). A week with my gf (which can be a mix of things) and then a week for myself (usually snowboarding or surfing somewhere by myself or a group of friends). But I can do this because I am divorced, and I don't have him 100% of the time with me. If I had, I could say goodbye to 'my' week (like I did while I was married).