It's hard to see your case, can you post a pic from the side? But you are right, there does seem to be a similarity. The dial looked strange which threw me off, but you are right it is likely a repaint.
A good source of info about Heuers from this period are the 1945 and 1948 catalogs, hosted on the main OntheDash website. I had a look through these catalogs and Heuer did make a watch that looks like your one, the Ref 406, and it was available in 18k gold (becoming the ref 416) or 14k gold (becoming the 415). So it looks like your watch could be based on the Heuer 416.
Most Heuer experts agree Heuer made watches for A&F, though you can read the heated exchange in a recent posting in the forum about this.
For info, the watch I showed I believe was based on the Heuer ref 346; here is the steel version of the one I posted:
And here is a reference 2444, also produced by Heuer:
