A million thanks to Millie, a reader who told me who that funny little character was!! A member of the Barbapapa family! I remember reading one of the books, even though nobody else in my family knows anything about it. They are a species created by Annette Tison and Talus Taylor, who lived in Paris. I found a page out of the book, The Barbapapa's New house, which is the book I remember.
They made the rooms by covering the papa Barbapapa (the big pink one) in cement, and then when it dried he would move and they'd do it again! I love it.
Images from someone else who had the same epiphany a few years ago.