If you're really worried about the "sex shops", all you have to do is avoid going into them. There are restrictions on what sort of items may be displayed in shop windows, there won't be anyone enticing you to enter the shops, no prostitutes will attempt to do business with you, and people who will be committing lewd and lascivious acts outdoors will wait until you have long since gone to bed. So stop worrying about the sex shops - just cross the street or avert your eyes. If your children have been exposed to cable TV and the internet, it's nothing they haven't seen or heard about.
The shot of the Eiffel Tower is possible, but it doesn't seem quite right, to me - given that it's about 6 kms away and not in a straight sight line from this address - I used the "Major Pigalle" shop address for reference. But I've seen Sacre Coeur pop up on certain streets, far in the distance, when I least expected it...
My concerns are that this apartment is on the top floor and has an elevator which will state that it holds 3 passengers, but in reality will only hold 2 "normal American-sized" people - not overweight, just taller and built differently from the tiny little French people who exist on espresso and cigarettes and live in buildings like this . This means that you'll have to make multiple trips up and down with luggage, since overloading an elevator this size will put it out of commission very quickly - are you prepared to haul yourselves, luggage groceries, etc up 6 flights of narrow, winding stairs several times a day? That's far too much exercise for me to even think about.
This apartment is not air-conditioned, will not have been insulated, and will be hotter than blazes, since the sun will bounce off the zinc rooftops. I believe the toilet is a "sani-broyer" - a noisy electric toilet which grinds up the waste - which are a very cheap solution but are notorious for not working properly. Since there's only one bathroom, you could be up that "proverbial creek" in no time flat.
Noise rises, so the apartment will also be noisy, if you do open any windows, since you're only a few steps away from a major intersection which unloads bus tours at Moulin Rouge all day and into the wee hours. There will be lots of drunks, a few discreet drug addicts, many homeless people very close to where you'll be staying - I'd worry more about them than about those sex shops.
The food choices frankly stink in this area, and there are very few supermarkets, so you'll have to rely on convenience stores or go to the Barbes outdoor market. If one of your goals is to save money on food, you could do much better. Transportation will involve making underground changes if you use Metro, and buses are not very convenient.
I would suggest getting a refund and looking somewhere else.
It's obvious that nobody lives in this apartment full-time, so it would qualify as illegal, if that's important to you.