If it were a Heuer...
...it would have something of a jumble of period references.
Rose gold case says 20s/30s, bar pushers pretty much any time before the end of WWII, but the hands say 50s/early 60s. The deeper Heuer shield is something more typical of post-WWII.
The case does have something of a 347 series (345 to 350) feel to it, as do some aspects of the dial but whilst I admire the guilloché finish on the dial, it's not something I'm familiar with Heuer having used. The printing of the Heuer shield over the guilloché looks hesitant - yes, it's difficult to print well on that finish but I'm not sure it sits well with the rest of the dial printing. I lean towards agreeing with Jeff and thinking that this was likely another brand that has been "repurposed" as a Heuer.