What kind of crankset is this?
This is a cottered crank. The chainrings are fixed to the crank and can not be moved to another, but you can replace the entire bottom bracket (combination of axle and bearings) and crankset. There should be no need to replace the front derailleur.

There is a risk that the bottom bracket shell is threade for an obsolete standard. To make any guesses if that is the case, we'd need to know the brand of the bike and width of the bottom bracket shell part of frame without any parts that are screwed in.