To understand understand the Paleocene world, one must first understand the concept of a recovery fauna. A recovery fauna is an assemblage of species that arises following a catastrophe of some sort. Local recovery faunas could include assemblages of pioneer species following a volcanic eruption, which form low-diversity ecosystems in the devastated areas. The Paleocene was a global case, in which every fauna on the planet was a recovery fauna. Nowhere was spared from the asteroid, and thus, during the Paleocene, the world would have appeared as an oddly empty place. The Mammal groups we know today had not yet evolved, so there were no Rodents, Carnivorans, Perissodactyls, or any other such animals, with the possible exception of Primates, which may have been present since the latest Cretaceous. Instead, the Paleocene was populated with leftover genera from the Cretaceous, making it seem more like a depleted extension of that period, rather than the first part of the age of mammals. Indeed, had one looked only at this period, one could be forgiven for getting the opposite idea, as giant flightless birds and other reptiles would have been by far the largest animals in these faunas, filling both the roles of large herbivores and apex predators.
Paleocene Europe would have been covered in dense rainforest, similar to this
The Mammalian faunas of the early Paleocene would have been almost identical to those of the late Cretaceous, but with far fewer species. Particularly hard hit were the marsupials, who in Europe were reduced from 9 to 1 genus. Placentals would have been common in this time, mostly consisting of small insectivores, primitive proto-Ungulates, and Primates or Primate-like animals. Another successful group was the Multituberculates, who, while now extinct, are in fact the group of Mammals that have existed the longest, spanning from the late Jurassic to the Oligocene, and thriving in Paleocene Europe. The Multituberculates did not belong to the same group as the Placentals and Marsupials, called the Therians, but instead seem to have been somewhere closer to the Monotremes, a group that today includes species such as the Platypus. The early Paleocene members of this group were superficially similar to rodents, but soon radiated into a variety of other forms, such as the North American Ptilodonts, which almost resembled squirrels. In Europe, a similar genus called Hainina would have filled roughly the same niche.
A Leptictid leaping into the air, from Walking With Beasts
Alongside the Multituberculates, Placentals were the other of the two most successful Mammal lineages in the early Paleocene of Europe. Already at the beginning of the period, Europe was home to a diverse assortment of Placentals, including the Pantolestids, an archaic group of semiaquatic piscivores. With powerful formlimbs and strong tails adapted for hunting in the water, they were a common group during this timeframe. Another successful group was the Leptictids, who had their origins in the Cretaceous, but survived the extinction and went on to become very abundant during the Paleocene. Small insectivores of the forest floor, the Leptictids' most unique trait was their bipedal gait, providing them with a method of locomotion similar to that of a Kangaroo. Probably the largest of the Paleocene Mammals were the primitive Ungulates of the time. Survivors of the K-PG extinction, these so-called "condylarths" were more basal than both the Artiodactyls and Perissodactyls, and possessed traits from both of them. As a testament to how odd some of the Paleocene fauna truly was, some Ungulates such as the Mesonychids were probably predators, though given their phylogeny, they were most likely actually omnivorous.
During the later parts of the Paleocene, several species entered the continent from North America, despite interspersal still being fairly limited at the time. Among these were the true Ptilodonts Liotomus and Neoplagiaulax, which joined the already present species Hainina. Condylarths continued to diversify, becoming some of the most common Mammals in Europe at the time. Primitive members of the group like the Arctocyonid Prolatidens, which were already present in the earlier parts of the period, diversified into a variety of forms, such as Landenodon, Mentoclaenodon, and Arctocyon. The latter in particular was an impressive animal, growing to be as large as a small bear. While an intimidating and powerful beast, Arctocyon was probably primarily herbivorous, only occasionally ingesting meat.
The Condylarth Arctocyon, from Wikipedia
While Mammals have been the focus of this post, this is a slight injustice, as they were not in fact the most common animals in the Paleocene of Europe. Reptiles of many lineages were far more numerous, and some even reached very large sizes. Amongst these were the Dyrosaurids, a group of archaic crocodiles which had survived from the Cretaceous, and were the largest marine predators in the Paleocene seas. On land, terrestrial crocodiles such as the Notosuchians were commonplace, arguably also leftovers from the Cretaceous. The most well known of the non-Mammalian inhabitants of Paleocene Europe however were the giant terrestrial birds, mostly belonging to the Gastornithidae, a group of large flightless Anseriformes. Chief among these was the bird Gastornis, While previously thought to have been a carnivore, Gastornis is now known to have had a primarily herbivorous diet, making it the largest herbivore in its habitat, probably only competing with other giant birds and the largest of Condylarths.
Gastornis and chicks by Charles R. Knight
Long as this post has been, I have still only covered a tiny fraction of the Paleocene fauna of Europe. While relatively empty compared to later periods, the ecosystems of the Cenozoic's first period were still rich and bustling in life, and describing them in their entirety in one post is neigh impossible. As there is so much more to learn about this fascinating lost world than I could ever hope to cover here, I will recommend a fantastic book on the subject: Mammoths, Sabertooths, and Hominids; 65 million years of Mammalian evolution in Europe, by Jordi Agusti and Mauricio Anton. You can get it on Amazon here