Resident in France, this is a remarkable little plain-turning lathe and, at just 200 mm long, far smaller than it appears in the pictures. The writer's opinion is that this would have been "home-made", though constructed by a skilled toolmaker.
Several points stand out: the headstock spindle runs in ball or roller races, the faceplate - as available on some high-class toolroom lathes - has circles of drilled or tapped holes; the leadscrew that runs down the centre line of the bed - but with a very small diameter knurled knob to rotate it; the bedways are screwed-on V-edged strips of steel;  the saddle is in bronze; the top slide has a very short travel, with both it and the cross-slide lacking micrometer dials; a fixed steady (also in bronze) is present, as is a 4-way toolpost with correctly-formed square tops to the clamping screws. The design of the set-over tailstock with the feed adjustment wheel set centrally, reflects practice as seen during the mid-1800s and, though of the lightest possible construction and cantilevered well forward of its base, is probably adequate for its purpose.