There will not be any kind of total ban called for - Finland is still largely forest and arable, and hunting is an old tradition (and a method of culling). The laws are actually quite strict - it is the application of them that is lax.
What we may see called for is a raising of the age at which a license can be issued, and restrictions on the types of guns that can be purchased and licensed. You have to remember that there is still compulsory national service, so most young guys over 21 are familiar with weapons. (except for those who choose civil service or are medically excused). I do not know if the young man in this tragedy had completed his national service. I suspect not. A macabre fascination with guns does not usually survive military training in Finland.
But there have been a number of incidents in the past year outside of professional crime. So a tightening up of regulation and monitoring is likely. You can't be me, I'm taken