The phonemicization of the nasal vowels in Galician-Portuguese happened probably in connexion with the loss of intervocalic /n/, a 11th-12th century process* ** first restricted to old Galicia (Galicia + northern Portugal), later carried into central and southern Portugal.*** Whilst those centuries corresponds also with a time when Galicia and Portugal were very open to French culture and influence (for example, Galician terms derived from Old French: think Cluny, navigation, Way of Saint James in Galicia, and French colonists in Portugal), probably to a larger extent that Castile was, I don't think that French influence by itself could be responsible for such an important development.
As for "r" [ʁ], etc, appears to be something genuinely Portuguese, since Galician preserves the old good [ɾ].
*) Some scholars argue that it happened before, but either they present as evidence charters copies centuries later, of local Germanic names where there is a alternation of forms with / without an n: Suebic Hermeric (5th century) / Gothic Ermanaric (4th century); Hermegildo / Hermenegildo, etc. Names as Hermeric and Hermegild also occur in Catalonia were intervocalic /n/ is always preserved (and where there were no Suebic settlement).
**) Off Topic: Most Galician varieties -but Ancarese- has dephonemized these nasal vowels, so Medieval Galician mão 'hand' > Western Galician man [ˈmãŋ] / Central Galician [ˈmãʊ̯/]. Still Galician sounds nasal if you compare it with Spanish, because in contact with nasal consonants vowels are heavily nasalized.
***) Clarinda de Azevedo Maia, ''Historia do Galego-Português'' (ISBN 978-9892614496), pp. 568-