Regarded as the father of the Finnish school of horn playing, Fransman was the last pupil of Karl Steigler in Vienna. While studying in Vienna, he lived with Steigler's nephew, Gottfried von Freiberg, who succeeded Steigler as principal horn of the Vienna Philharmonic in 1932.

He joined the Helsinki Philharmonic as the third hornist in 1932, and became principal horn in 1937 where he continued as principal until 1967. Fransman was one of the most outstanding Finnish orchestral musicians, but the more influential part of his life was as a teacher at the Sibelius Academy (1931-1973).