According to C. Paul Cook, Ph.D., of the University of Toronto, neologisms, newly coined or newly formed words, are of three types: "lexical blends and ameliorations and pejorations."
A popular example of a pejoration is "poetaster," which uses the Latin suffix combining form -aster to render a "poet" ( Middle English < Latin < Greek) an inferior shadow of a true poet. Pejorations are derogatory, disparaging words or expressions.
A popular example of an amelioration is the word "nice" (Middle English < Old French) which once was a pejoration meaning someone who was excessive in fussy and finicky tastes. Ameliorations were originally disparaging pejorations but have been linguistically "elevated" to a new complimentary meaning, such as the current definition of "nice": "great accuracy, precision, skill, tact, care, or delicacy" (Random House/American Heritage).
A current example of a new lexical blend, used by Cooks as an illustration, is "cosmeceutical," which blends Greek origin "cosmetic" with Late Latin < Greek "pharmaceutical." Neither of these are combining forms; this is why they form a lexical blend (from word classes that have lexical meaning) rather than a combined-form word, e.g., microbiology (micro- Greek combining form; biology German loan word).
A neologism is a new word, a new word meaning for a familiar word, a new word usage for a familiar word, or a new phrase (Collins Dictionary). When a word becomes an amelioration (is elevated), loan words, or foreign word borrowings, are not directly related to the amelioration process. Yet, if the ameliorated word morphemes are themselves loan words or combining forms from foreign borrowings, then foreign borrowings are indirectly related to neologisms of the amelioration type (for example, if poetaster were elevated to an amelioration).
When a pejorative is newly adopted, like "economism," the same description of indirect involvement of foreign borrowings applies. "Economics" is a familiar word. When it develops into the pejoration "economism," the Greek suffix -ism is added to the Latin < Greek root "economics." In this way, two foreign borrowings are indirectly involved with this pejorative neologism.
Lexical blends are developed from a similar indirect involvement: they are neologisms formed from existing familiar words, i.e., "cosmetics" and "pharmaceutical" that may have come from foreign borrowings themselves
A hypothetical illustration of a direct involvement of foreign borrowings would be forming a neologism from French beau and Greek gape. These foreign words are used in English in their foreign context; they have not been incorporated into the English lexicon the way, for example, "imagination" and "resistance" have been.
If I borrow beau and gape to create the neologism beaugape, meaning "fine gift" (as in "I need a beaugape for the party, not just any present"), foreign language borrowings play a direct role in coining the original (not previously familiar) neologism.
[C. Paul Cook. "Exploiting linguistic knowledge to infer properties of neologisms." University of Toronto. 2010]
Some definitions of neologisms do not include foreign words. Instead, words borrowed and eventually kept from foreign languages are called transfer words, borrowed words, or loanwords. However, given the broad definition of neologisms as "a newly coined word that is in the process of becoming commonly used but not yet widely accepted," a loanword or foreign word transferred from one language to another does qualify as a neologism.
But such a word ceases to be a neologism (neo meaning new) when it becomes widely accepted. In other words, when it becomes "old" it is no longer "new" (neo).
Some examples are musical terms from Italian such as allegro, tempo, aria, and soprano.These are no longer neologisms because they are widely accepted, but when they were beginning to be used in English, they were still neologisms. That's why it is better to think of a neologism as a phase in a word's history; not a concrete, changeless state. Once a loanword is accepted, it also is no longer a loanword because it's kept rather than "on loan."
Sometimes a neologism has to be translated. "World view" comes from the German "welt anschauung." "Déjà vu" (French) used to be a neologism but now is widely accepted in English and it has not been translated, so it has kept the French spelling.
Neologisms often emerge when two cultures with different languages interact. The more interaction, the more word sharing. When the Normans invaded England in 1066, the French and English languages interacted quite a bit and that's why English today has a lot of Old French and Anglo-Saxon (Old English) roots.
A more modern loanword, which is no longer a neologism because it's widely accepted, is "paparazzi" from the Italian.