This answers the time question, but how about the range. Before erectus, they all seemed to be confined to Africa, while modern man is all over. How about the three predecessors?
Neanderthals lived in Europe up until around 20,000BCE. That's why we call them that:
Neanderthal is the German name of the Neander Valley, near Düsseldorf. They normalized German spelling in 1901 so Thal is now Tal, but they didn't change the name of the species. The H is silent, there is no TH sound in German.
The valley is named after the writer Joachim Neumann. He wrote under the pen name of Neander, which is the Greek translation of his surname, "New Man."
Homo sapiens and H. neanderthalensis lived concurrently in Europe for some time. I'm not an anthropologist but from what I've read I gather that it's pretty well accepted that when sapiens arrived they interbred with Neanderthals, so modern humans have some as yet undetermined quantity of Neanderthal genes.
That original wave of modern humans are not by most reckoning the ancestors of today's European peoples. Most of those people are descended from the Indo-European tribes who didn't arrive until very roughly 4000BCE, the Celts being the first tribe to set foot on the continent. Even more recent arrivals, during historic times, are the Turks, Magyars, Huns and Finns (including the Estonians and Saami, formerly called Lapps), all Mongolic peoples, at least by language. The Bulgars are recent, although no one can identify their bloodline, as are the Jews, a Semitic people.
The only people we can name who were already there when the Indo-Europeans arrived are the Basques, who are still hanging on, the Etruscans, who are long extinct, and the Picts, who were once the people of what is now Scotland but were culturally overrun by Celts. We can fathom nothing about the origins of these people. Same goes for whoever built Stonehenge.
However, from archeological digs we do know that there were several waves of migration into Europe, mostly through the Caucasus region but possibly to some extent also across the Bosporus and even across the Mediterranean. The Basques etc. are almost surely not the original Homo sapiens who encountered the Neanderthals.
Notwithstanding all that, each wave of migrants intermarried with the previous settlers, so there are still Neanderthal genes in modern Europeans.
Jean Auel's series of novels beginning with
Clan of the Cave Bear is set at the end of the last Ice Age when Homo sapiens immigrants first encountered Neanderthals in Europe. The story is pure fiction but it's as good a guess as any as to what it was like when the two species finally met. She did a lot of research, including living alone as a Stone Age human in a remote Alaskan winter to see what it felt like. So her anthropological and scientific details tend to be very accurate and it's interesting just for that. Although science marches on: when she wrote the stories it appeared that the Neanderthal brain had no speech center, so her Neanderthals speak in sign language, which is a major plot device. It turns out that was wrong and they could have developed speech.