Moving from R22 to R410a
Since you're changing refrigerants, it's recommended to replace the condensing unit (outdoor unit), all the copper refrigerant lines, as well as the evaporator coil (inside the furnace).

It's possible to keep the copper refrigerant lines, though it will require a bunch of extra work. And even still, not replacing the lines can reduce the life of the new unit.

Depending on the new evaporator coil, it may be able to be fit on the existing furnace.  However, if the furnace is old and inefficient, it's a good time to consider upgrading to an efficient unit. The evaporator is not part of the furnace, though it's typically connected to it. So it is possible to change the evaporator, without replacing the furnace.