Probably not exactly or at least not exclusively what you're looking for, but while you're at it, you might want to take a look at this multi-volume series of song books called
Suuri toivelaulukirja, which has tried to keep tabs on the most loved popular songs in Finland:
http://www.suomalainen.com/webapp/wcs/s ... laulukirja
This page lists the table of contents (titles of the included songs) for each volume in the series:
http://www.f-kustannus.fi/suuri-toivela ... sluettelot
The series of books spans several decades. Each volume contains simple piano and sing-along arrangements of the included songs, and lyrics too, of course. Many folk songs are included in that lot and much of it is Finnish music, but it is not exclusively about folk songs or Finnish-originated compositions; there are many other popular songs as well (Christmas songs, songs from popular musicals, etc.) The older volumes (with the lowest ordinal number) are probably better in that folksy and traditional emphasis than the most recent ones.
If you visit a Finnish used books store (or see what is available online), you could also find old song books used in schools in the 1940s...1960s... those are also likely to contain many simple sing-along arrangements of traditional folk songs or other "traditional" music.