I said it was acceptable, just not the best. There are very few online references using What with cost - it is usually paired with how much unless referring to the cost of living/war/raising kids/renovating etc - kind of in the sense of a collective price = cost, (and in this phrase often infers costs other than financial obviously)
What is usually paired with price - to my ears, the proposed sentence is a bit like How much is the price of this sofa but English is very regional and perhaps where you live, it is common to ask the price the way it was suggested.
Re me "sticking strictly to french", in my comment, I said there were lots of ways to ask the price. I was merely pointing out that if a heart was taken, I thought, from what I knew and had researched, it would be because Combien translates more closely in this sentence to how much not what.
I assumed the question was posed because the asker had lost a heart so he/she thought it was bad english. I was trying to point out that it wasn't, but nor was it the best translation of the french.
Oh my...in the US (at least my part) we rarely use settee in normal speech, and a "lounge" is a room, not a piece of furniture. Usually it is couch or sofa. To add another word to the discussion, you will at times hear older people say "davenport", but that word has fallen out of use in recent years.