That's a very tight connection, however, silver lining for your going out of JFK is that JetBlue is always delayed, so that might help you out a bit. Are your bags being checked through for you or do you have to pick them up at baggage claim and re-check them at JetBlue? I know many airlines have codeshare partnerships for this reason, but I'm not sure about Finnair and JetBlue.
Tight connection