Fallen Feline

No. A spell already on the chain has already started its play because playing a card means placing it there and queuing it for finalization.^420.1 While Fallen Feline is at a battlefield, it prevents opponents from starting another play of a spell with the chosen name, but it does not stop the spell already on the chain from finalizing or resolving.

If that spell later instructs an opponent to play another spell with the chosen name, Fallen Feline can still make the new play impossible without preventing that spell from finalizing.^358.3.a The play instruction is negated, so the second spell stays in its current zone.^359.3.e.6 The spell already on the chain continues resolving and does as much as it can.⁰⁵⁵

You can react before its controller names a spell, but once the name is chosen, it is too late to start playing that spell while Fallen Feline remains at a battlefield. The name is chosen only when the play effect resolves,^355.18 after players have had the opportunity to react to the finalized ability.^407.4