A few notes.
These perfect constructions tend to lose their resultative meaning with time, and so languages may develop fresher, originally more expressive, replacements instead. For example, Spanish and Portuguese at their current stage use both the older perfect with “to have” and a newer one with the etymological “to hold” — like for example the Spanish lo he hecho “I have done it” and lo tengo hecho ‘the same’, etymologically “I hold it done”. The exact relationships between both variants are different across the varieties of Spanish and Portuguese, but eventually the newer form is going to win, I guess.
On the other hand, these perfects with the passive participle and ‘to have’ are an option when the colloquial language (where such forms evolve) lacks a formalized distinction between active and passive past participles, like in Germanic and Romance. Where such a distinction is available, another perfect may evolve, the one with ‘to be’ and the past active participle, “I am who-has-done”, like in Baltic, Baltic-Finnic and historical Slavic languages (a millennium ago Slavic even had two past active participles, one of which was specialized for the perfect tense while another one remained independent). In modern Slavic languages past active participles have either disappeared or are no longer freely used in the colloquial speech, so these languages may develop a newer perfect, this time with ‘to have’ and the past passive participle. Macedonian has both variants, the older ‘I am who-has-done’ and the newer ‘I have it done’, codified in the standard language as synonyms.
Overall, I don't think that influence between languages is of any special importance here: such constructions are natural, they easily develop in the human speech, and easily disappear or get renewed with more expressive synonyms as time passes. For example, colloquial Russian doesn't use ‘to have’ and hardly has had any Romance or Germanic influence, yet it too has developed a newer perfect, of the type ‘at me it is done’, that is (1) with a past perfect participle on the one hand, but (2) with a Russian counterpart of the ‘to have’ construction on the other.