A very old and difficult question. The real answer, I believe, is: UNPREDICTABLE! The arguments of the supporters of the free carrying of weapons: the presence of a barrel in a citizen makes the criminal think how not to get a bullet in the forehead and crime will decrease. The arguments of the opponents: in Russia there is so much drinking and such a number of drunken conflicts that they will be “fired” for or without reason, and crime will increase. Both factors, in my opinion, have a real impact. So which one will win in that direction and the crime will change.
The number of crimes involving firearms is highly dependent on the general social characteristics of the country. It is clear that you cannot compare Colombia and France.
But statistics show that, for example, in the USA, where firearms are more or less freely available to the population, the number of "domestic" murders is significantly (several times) higher than the average for countries with an equal level of welfare .