Fujifilm's recent cameras take their design cues from rangefinder cameras of the 1960s, 1970s, and 1980s. At that time, a look similar to this was typical, just as DSLRs in the 2000s tended to be rounded blobs of black plastic or today's smartphones are mostly shiny black rectangles. Therefore, there are many candidates, but I think perhaps the closest is the Canonet series, like the Canonet GIII QL17. Many of these were made, so you should be able to find one for sale, although maybe not quite at your price point.
Photo by Hiyotada, CC-BY-SA 3.0
And you don't have to take my word for it — Digital Photography Review made the same comparison in their review of the X100, the model with which Fujifilm kicked off the X series and its styling.
The Olympus 35RC also appears in that review, and it'd be another good candidate, as are many classic Olympus Pen models. Basically, the silver-and-black styling was common for everything at the time, and you just need to narrow it down to rangefinder-style cameras, and then to the boxier of those (the Minolta A, for example, fits the color scheme, but is much curvier). And the classic Pentax K1000 has the color scheme, but the SLR pentaprism means it's not a direct match.