This 'early semitic influence on Germanic languages' is a 'popular' speculation. That is popular with very few scholars, linguists, but apparently a good seller.
After listing a few similarities between semitic (modern Hebrew, as it seems) and Germanic languages, McWhorter specifies this, 'his' hypothesis:
Okay—maybe. But what we want now is evidence that speakers of a Semitic language from way down in the Middle East actually migrated to the northern shore of Europe, namely, what is now Denmark and the northern tip of Germany, or the southern tips of Sweden and Norway right nearby. Here, the evidence helps us only so much.
We can know which Semitic speakers are of interest: it would be the Phoenicians, whose homeland was in today’s Lebanon, Syria, and Israel. Their language, now extinct, was especially similar to Hebrew. The Phoenicians were one of those peoples of ancient history who were seized with a desire to travel and colonize, and they did so with great diligence on both the northern and southern shores of the Mediterranean, taking advantage of their advanced sailing technology. This included major colonies in North Africa, at Carthage, as well as one as far west as Spain, in what is now called Cádiz.
The Phoenicians even rounded the bend northward up into Portugal a tad . . . but there, the record stops. Did they sail up past the British Isles and round past the Netherlands to hit the neck of land shared today by Denmark and Germany?
There is no record that they did so. Apparently they were very secretive about their ship routes. Also, many of the northern European coastal regions they would have occupied have since sunk under the sea. This leaves us having to make nimble surmises.
That missing record bit is correct.
No historical evidence, no archaeological evidence, but a few linguistic peculiarities. Let's look at the linguistic claims.
Substrate speculations
Theo Vennemann posits a Semitic substrate for Proto-Germanic, an encounter made possible by Phoenician colonization of the North Sea area. Among the supposed loanwords are the names of the Germanic gods Pol and Baldur, none other than the Semitic god Baal. Vennemann’s vast work on Semitic and Basque substrates in Europe seems to be politely tolerated but generally ignored by IEists, and I heard of this hypothesis from the popular press: John McWhorter’s Our Magnificient Bastard Tongue: The Untold Story of English. McWorther does mention that there are serious objections to this theory, but in my opinion, even bringing it up at all risks leading impressionable laymen astray.
Christopher Culver: "Substrate speculations", 2012
The relevant article on Wikipedia is Atlantic (Semitic) languages.
Venneman as the originator of this theory introduced this concept of a proposed pre-history of Europe after presenting the very notable hodge-podge of linguistic observations with the following introduction:
"So far, I've expressed myself as a linguist. I could and should end here ... No linguist can answer this question for these prehistoric processes, only a prehistorian with reference to archaeology and - for a later phase - possible ancient testimonies. So everything I say now, I say without any professional qualifications. This gives me the advantage of a certain fool's freedom and allows me speculations that would probably forbid the expert from his scientific ethos. … These are speculations evoked by hard linguistic compulsion in a soft prehistoric space." (from 1984, quoted after p168, my translation)
Michael Meier-Brügger: "Indogermanische Sprachwissenschaft", deGruyter: Berlin, New York, 92010.
And factoids here is in that sense:
"Factoids – a word coined by Norman Mailer in his introduction to Marilyn – are mere speculations or guesses which have been repeated so often that they are eventually taken for hard facts. There is something decidedly unbiological about such factoids: the tendency to get stronger the longer they live is one of their most insidious qualities. Factoids occur in all branches of scholarship ... The process by which mere hypotheses at- tain the apparent rank of established fact, without ever having been proved, presents a linguistic and a psychological aspect. Linguistically, words or particles indicating the hypothetical character of a statement are dropped one by one in a process of constant repetition. The subjunctive is exchanged for the indicative, and in the end the factoid is formulated as a straightforward factual sentence." (F. G. Maier: "Factoids in ancient history", JHS 105, 1985, 32-39)
In summary: there might have been quite some traders from all over the world in northern Europe, but very few if any migrants in pre-historic Europe during the iron-age. Earlier of course the post-ice-age re-settlement, the spread of agriculture and the (proto)-indogermanic expansion might account for something in terms of linguistic development after all. Coming from the East, South-East: The Vasconic hydronomy thesis cannot be disproven, or proven, but remains the stronger part of this argument.
But the proposed hamito-semitic linguistic contact – in the proposed dimensions – from Phoenician times is not in accord with any archaelogical evidence, much too late, and very weakly argued for in the first place, if not outright 'no-where outside of fantasy'. In any case, this linguistic semiticism had not much connection to "Jews", "Ashkenazi" etc.
As the article Genetic Roots of the Ashkenazi Jews already states, at the latest but not that much earlier than from Roman times onward a significant number of also semitic-language-capable people spread into Germanic lands. And then Yiddish evolved as a mainly German-Hebrew hybrid, with both Hebrew and Yiddish giving back a lot into variants of German.
The historical records for "Jews in Europe" is quite spotty, but very much confined to Roman and Greek sources. Early presences are only 'confirmed' in legends of Jewish captives brought to the Rhine by Romans, an early rabbinic council in Trier at the time of Jesus' death ((note: "Rabbinic" makes this assertion anachronistic per se)src) or a equally mythical presence in Prague "before the destruction of Jerusalem" (src). As Proto-Germanic is said to be dated
It is possible that Indo-European speakers first arrived in southern Scandinavia with the Corded Ware culture in the mid-3rd millennium BC, developing into the Nordic Bronze Age cultures by the early 2nd millennium BC. Proto-Germanic developed out of pre-Proto-Germanic during the Pre-Roman Iron Age of Northern Europe.
The conclusion is that there are no historical records connecting these two points in time. What speaks in favour of semitic-language speakers in contact with Northern Europe is the vast trade networks that must have existed before, but we have evidence for in bronze age times, namely to Cornwall/Devon and Saxony/Bohemia regions in Europe, as people did go to some lengths for tin:
(src)
But how much influence those traders could have had on the development of a language in its most basic forms (specialty vocabulary is another matter) is illustrated, nicely, but indirectly, here:
Jan van der Crabben: "Greek and Phoenician Colonization", Ancient History Encyclopedia, 2012
Which leaves quite the gap compared to this: 
Also keep in mind that the existence of 'Phoenicians' as a distinct cultural group speaking a uniform semitic language, forming something like a 'nation', is no longer an uncontested concept; further weakening the original linguistic hypothesis. Neither were these 'semitic people' the only people trading, not were they so much really identifiable in the desired time-frame either.
“Phoenician,” then, was not deployed in Greek and Roman literary sources to designate an ethnic group in and from Phoenicia. In its earliest usage, it was simply a vague term for Levantine sailors who spoke a distinctive language, and Greek authors tended to emphasize a wide range of similarities, geographical connections, and family relationships between these people and their own. The fact that the toponym and ethnonym do not map onto each other in several Greek sources—the wrinkles in the intellectual logic—suggests that the Phoenicians were not identified by their neighbors as a specific people a ached to a specific place, culture, or history. The Phoenicians were first perceived as having a more distinct character in the late fifth century BCE, in the context of tensions between Carthage and Greek-speaking cities in Sicily. In the Roman period a stronger and sometimes more negative stereotype emerged, but there was still confusion over the appropriate vocabulary: phoenix, poenus, and punicus were used to designate a variety of Phoenician-speaking groups, and there was in particular a distinct tendency to use the adjective punicus in relation to North Africa as a whole, not just its Levantine inhabitants or settlements, and to the Phoenician language.
Josephine Crawley Quinn: "In Search of the Phoenicians", Princeton University Press: Princeton, Oxford, 2018.)
