One point of contact is the word for 100--sata in Finnish, sada in Estonian, and szaz (pronounced "sahz") in Hungarian...all derived from a form similar to the Avestan (Old Persian) word satem meaning "one hundred." Maybe that means the Proto-Finno-Ugric speakers didn't have a word for 100 until they came into contact with the Proto-Indo-European speakers. Or maybe they just thought the PIE word was cooler.
“Finnish contains borrowings from all stages of Indo-Iranian, that is from Pre- and Proto-Indo-Aryan (precursor of Old Indic ~ Sanskrit), from Pre- and Proto-Iranian, from Pre– and Proto- Balto-Slavic as well as Proto- and North(-East)ern Baltic, and last but not at all least from all stages of Pre- and Proto-Germanic development.
The very earliest borrowings appear to come from a dialect close to Proto-Indo-European (PIE) itself. In some of these oldest borrowings speakers of Finno-Ugrian have reproduced so called laryngeal (‘H-like’) sounds of PIE, which later disappeared from all IE languages except Hittite and its closest relatives. Borrowings with laryngeals which appear only in the western Finno-Permic languages, often only in Baltic-Finnic or in Saami (“Lapp”), may also originate from an early Pre- or Proto-Balto-Slavic IE dialect, a dialect which may well have been a very archaic one in comparison to others within the Indo-European language family a couple of millennia B.C.”
http://tcoimom.suntuubi.com/?cat=10
Lexicon of Early Indo-European Loanwords Preserved in Finnish
http://kotisivu.lumonetti.fi/js749/lexicon.htm