English is a language with Germanic roots but with a vocabulary heavily enriched by French and Latin. There is nothing improper about using words with an etymology based on a Romance language.
According to the Online Etymology Dictionary, the root of "implicate" is the Latin verb "implicare" meaning "involve, entwine, entangle, embrace." That is also the root of "imply." So to use one but not the other because of its Latin origin is absurd: they both derive from the exact same Latin word.
The mathematical meaning of "imply" is synonymous with the verbs "entail" and "prove." But that is not the only, or even the most common, meaning of "imply." Far more common outside mathematics is the meaning of "suggest, but not explicitly." The restricted sense of "imply X" is "show that X is a mathematically necessary consequence" whereas the more common sense of "imply X" is "suggest that X is true without explicitly saying so."
According to Merriam Webster, "implicate" may also have the meaning of "entail" or "prove." However, it is normally used to mean "to bring into incriminating connection." In other words, it is primarily used in a legal or quasi-legal context to suggest culbable involvement in a crime. For example, "This new evidence implicates Smith in the murder of Jones" means that "This new evidence suggests that Smith was a party to the murder of Jones."
To avoid ambiguity, my suggestion is to use "entails X" to mean "necessarily results in X," "implies X" to mean "suggests X, but not explicitly," and "implicates X" to mean "gives reason to believe X is guilty."
EDIT: I wonder if your concern about "implicate" comes from the fact that "implication" does frequently mean "consequence." This is a case where the meaning of the root verb and its derived noun have drifted apart.
EDIT 2: You may have been advised at some time to prefer the synonym with the Germanic root over the synonym with the Romance root. For example, you may have been advised to say "house" or "home" rather than "residence." The advice is good in most cases: many residences are apartments rather than houses, and it is a rare prisoner who uses the word "home" to refer to his cell, which undoubtedly is his residence. The reason, however, for this preference is not etymology, but clarity. Use the word that best fits your intended meaning regardless of etymology.