Hottie did when I lived in a house with that floor type. I had to keep his fur really short on his paws. Hottie fell going down the stairs and then blamed the landing as " the dangerious part". He sleeps with me, and would stand at the bottom of the landing and bark . I put short little runners down. It helped but he was still suspecious. Little by little he came around.
I am sure you already have the nails short, so take a look at the paws for side hair around the paws and underneith. Some poodles have alot of fur on the pads. Also if you wash the pads, it will raise the natural padding " flesh" cleaning it, and it will grip more. Do not soak the pads- just a wash.