This is excerpted from the IMSLP copy of Devienne's Flute Concerto #3 in G (middle of page 3). In the beat pointed by the arrow below, it's pretty obvious that the intent of the dot is to make the first quarter note extend by a sixteenth note (as opposed to the modern meaning of a dot, which is strictly to extend a note by half its length). Is this common usage in scores of that time?
Note also how in subsequent measures we see a dot after a quarter note but preceding 2 sixteenth notes instead.
While it could have been a triplet as @JohnBelzaguy suggested, and as @AndyBonner observed how in page 4 starting at the 6th system there is 10+ measures run with 8th note triplets notated without the "3", after listening to a sample performance below
where the tutti passage in question starts at minute 3:48 where Violin 1 doubles the Flute, we can hear clearly that it is performed as a quarter note tied to a 16th note.
This is also in character with this Mozart-like late-classical period piece (first published in 1785) where we would not see a mixing of triplets and regular values during a single run. In the snippet's context, the runs are predominantly 16th notes, making 16th note triplet not only too hurried but also out of character for the classical elegance. Therefore it makes sense that the orchestra played the three 16th notes as strict 16th notes, not as a triplet.
Conclusion: The notation at the time may not be as strict as today, and the OP assumed the meaning correctly that the dot's value is 16th note duration.
I haven't seen this before, but I have to say I don't find it particularly surprising. The meaning of the dot was somewhat in flux at the time; I don't remember when double-dotting was invented, but I think it was somewhat later, and it's fairly well established that a single dot in the high baroque is often intended to lengthen the note by 3/4 instead of by 1/2.
(For example, some parts might have dotted quarter and eighth while others have quarter, dotted eighth, sixteenth, and it is really rather more natural to play the first rhythm double-dotted so the last note is simultaneous in all parts.)
If the dot was seen as flexible, it makes sense that it could be shorter, too, as well as longer. And while it might make a reader do a double take on the first encounter, it's still quite clear what the composer is communicating, as you note in the question.
Modern convention, of course, would call for the quarter to be tied to a sixteenth instead of what we see here. But note that this is French, and the French were particularly renowned for notes inégales, ("unequal notes") a sort of subtle swing rhythm. Since the basic approach to rhythm was explicitly opposed to metronomic regularity (which it was everywhere, but even more so in France), it is particularly unsurprising to see this liberty being taken in a French composition.
John Belzaguy notes in a comment that the 16th notes may be intended as a triplet. This is of course quite possible. One would want to check other sources, if there are any, for evidence supporting that (for example, a 3 in a manuscript that was somehow omitted from this engraving). Another possibility is that the composer did not feel any need to mark the triplet explicitly because of the aforementioned rhythmic flexibility of notes inégales. Someone with more exposure to the French literature of the period (Andy Bonner?) may be able to shed more light on the question.
