What species in central Europe in the phylogenetic tree shows the closest difference in time to the most recent common ancestor with Homo sapiens?
I am not sure I understood the question. Is the following your question?
Among all species living in central Europe, which one is the most closely related to homo sapiens?
Source of information
opentreeoflife.org (nice vizualisation on OneZoom.org) is one of the most update synthesis of existing research inn phylogenetic reconstruction. I base my answer in consideration of the tree on OneZoom.org.
Outside Homo sapiens, there is no living primates (or any other Euarchonta) in Central Europe. The sister branch of primates include Lagomorpha (Hares and Rabbits) and Rodents (mice, rats, squirrels, prairie dogs, porcupines, beavers, guinea pigs, hamsters, and capybaras). In other words, any Lagomorpha and any Rodents are all equally related to any Primate (incl. Homo sapiens). Their Most Recent Common Ancestor (MRCA) lived about 75 millions years ago.
How about Hedgehogs?
Hedghogs are Insectivora and they are a sister group to all primates, lagomorpha and rodents. Their MRCA lived about 80 million years ago. So, no there are species currently living in Europe that are more closely related to us than hedgehogs.
The term "next relative" does not mean anything! You might want to understand your understanding of phylogeny with an introductory course.