No, and in fact, Poodles tend to be more scared of even small dogs than cats.
Information to include in the answer: This story likely originated from a drawing of an early European dog found on a tomb painting dated 1427 AD which shows two large hunting dogs with lances. These drawings were based on the association between medieval hunting equipment and nobility – or that is, most nobles would have owned hunting dogs around this time period – and we know for certain that they did not hunt bears…