Since you are changing cranksets, I'd resize the chain just on general principles. It doesn't take very much time or effort to do. I use the big/big method. Run the chain around the biggest front chainring and the biggest rear cog bypassing the rear derailleur. Figure out the shortest place that you could connect the chain. Now add 2 links (1 inch) onto that. That s the shortest chain that you can safely use with that gear combination. If it was my bike, I'd start a brand new chain with the new chain rings.

Going from a 52 to a 50 isn't much of a big ring change. Your front derailleur might work just fine as it is. If it was my bike, however, I'd lower the derailleur a skosh to match the new smaller ring.