The case has some features that are similar to Heuer cases, but it's not jumping out and shouting that it's a specific Heuer case to me. It could be a 403 but always worth bearing in mind that a lot of manufacturers were using very similar cases in this period. It looks worn and/or polished so original features are perhaps not standing out as much as they might.

The second hand is clearly anachronistic and I agree with Darren that the timekeeping hands are too small. Heuer did use similar hands on the 10.5 ligne (~24 mm) movement 5408 so they could come from that, but again bear in mind that hands like these were in quite common use. The "tail" on the needle in the 30 minute register is much more characteristic of other brands than it is Heuer.

The dial is the biggest concern. It looks very strange, as if it's been ground right down judging by how the registers just look stamped into the dial face. And the markers, both stick and arabic, look like they're embedded in the dial, which I don't think I've seen on any other Heuer. And the lume plots look like they've never actually been lumed, a frequent sign of refinishing.

And then we come to my biggest problem with the watch. That arrow on the Tachymetre scale is very 30s and 40s. It's down to the Tachy scale decreasing as time increases, so perhaps they felt early users needed assistance with what direction to read it in but later on were given a bit more credit. Other manufacturers stuck with it as a stylistic measure for longer, but Heuer definitively didn't. Ok so far, that matches the period of the hands. But. And it's a big but. The font used on the registers is definitively what was used from the 1960s, not earlier. And if you look at the launch Autavias and its contemporary 404s et al, you'll see that they don't use that font either. In fact, it's not until the Carrera comes along in 1964 that we see it become the default for Heuer (as well as just about everyone else making chronographs, it looks to me like Singer and their competitors used the same style on all their clichés and you got what you were given. Even if you were Rolex).

So we have a 2 decade disconnect between two features of the dial. Makes it a clear redial for me and with the other questions around components of the watch, it's hard not to see the whole as equally questionable. As Darren said though, it would be good to see movement and the caseback inside and out to make a final call.