Hi Thomasz,
You're right, you'll add to do some customization in order to get what you want .
The best way in my opinion is to select image and description as "item layout" for the carousel and then modify it.
Once you did it, go in Display>Views and find "listing_img_desc" for product.
Caution! If you are using this layout somewhere else, find another that you are not using and copy paste the listing_img_desc code inside the file (for example listing_title)
Here is an example of the code you can end with. It's a two column table so I just move the text column to the left (you'll have to add some css to fix the width) and moved some element from the right to the left (such as the add to cart button and so on...). Feel free to do what you want with the informations!