Searching for images of this powered balloon, I found this one, which happens to have a description in french that says :
A. Aerostatic globe 27 feet in diameter filled with flammable air and
attached to circle a, b,
B. Parasol of 18(?) feet in diameter whose branches are held to the
axis or handle by the strings. d.d.d.and are spread out from the
circle a.b. to gather all in c. Note, it should only be used to
support the machine in the air in case of accident to the globe in
order to avoid a violent fall.
C. Vessel carrying the passengers suspended and fixed to the axis or
handle of the parasol.
D.and E. Fins or wings moved alternately by the passengers by means of
the branches e.f. fixed to the axis or axle of the wings, those marked
E are open and pull on the air to make the the vessel to move forward
at will, and those marked D are closed since they act in the opposite
G. Fins or wings seen from the front, the upper one is closed and the
lower one is open. Note: The strings g. are used to prevent the wings
from opening too much or tipping over and hold them by means of the
support h. as the parasol is held by the strings d.d.d.d.
In 1784 metric system was not there yet. According to wikipedia, at the time in France one foot was 326,569mm from 1668 to 1799.
Therefore, the balloon is 8,77m in diameter, 353m3 in volume.
If the gaz is hydrogen, it can lift 423kg.
Its frontal area (disc projection) is 60,4m2.
Coefficient of drag of a sphere 0,4
Let's assume the rudder starts being effective at ~10km/h, or 3m/s
The force needed to move this sphere at a constant 10km/h fighting against its drag is 1,365kN
The propelling method using reciprocating folding leaves-look alike, named D. and E. do not seem efficient compared to a propeller, yet it still moves some mass of air.
Any propulsion method that achieves to move a mass of air in the desired direction is effective, which does not mean it is useful.
For instance this powered flying vessel may very well propel itself and navigate using its fins, and rudder, inside a large hangar.
However if it flies outside it will have almost no authority against the slightest breeze.
---- somehow I'd love to see a test of the 18ft diameter parasol safety device ----