Cortex M0 - Defining an interrupt routine in assembly
How do I change the address at the above entry to point to the start address of my assembly code so that I can handle the interrupt in assembly?

Asssuming default startup, just declare the function with the correct name in assembler:
.syntax unified
.thumb
.arch armv6m
.text

.global TIM3_IRQHandler
  .thumb_func
TIM3_IRQHandler:
  BX LR
.end

Note: This example will deadlock (read: infinitely tail-chain), since the timer flags are not resetted properly.