The Merovingian is an extremely old program. The Oracle described him as being "one of the oldest of us".
According to the Wikia for The Merovingian he is said to have a connection with the second failed matrix.
A connection between the Merovingian and the second failed Matrix may
exist. The Merovingian surrounded himself with henchmen with
remarkable abilities that other programs do not show. The Oracle,
Persephone, and the Architect alluded to these programs in various
conversations involving Neo. These programs inhabited the ill-fated
second Matrix in an effort by the Architect to establish a primitive
level of choice through frightening the human populace. When the
second Matrix failed, the Merovingian kept many of these old programs
for his own devices.
Now as far as his powers it's because he is skilled in rewriting code, his original role prior to exile was to act as the Operating System.
It has been confirmed that the Merovingian's prior purpose to exile
was the Operating System (like Microsoft Windows or Mac OS X) for an
earlier version of the Matrix, the second of the two Matrix betas.
Thus the Merovingian's original role was a leadership position,
coordinating activity and information in the Matrix beta. He would
later make good use of these skills in exile as a power broker and
trafficker of information. It also explains why the Merovingian is so
skilled at rewriting Matrix code to create new custom objects.
As revealed in the Matrix Online:
The particular quote that is from the Matrix Online is as follows from Theories of the General. (The blog was supposed to be an in character Matrix Online Character's blog that supplements and adds backstory information... It was written by Matrix Online Storywriter Paul Chadwick.)
Theories of the General (July 26, 2006) - The Kid presents a few
theories about who the General is. He says he could be a misfit
program who genuinely wants to help humans, or he could be a tool of
the Machines. But he discredits both of these theories and leaves the
question open. The Kid says something else that sheds quite a bit of
light about the history of the Merovingian:
True, appearances do lie. There's no reason a sun-controlling program should look like a little girl. Or an operating system seem to be a sybaritic French gangster.
The first sentence refers to Sati of course, and the second sentence refers to the Merovingian. The second sentence confirms my theory that the Merovingian used to be the Prime Program for Matrix versions 0.8b and 0.9b (see Matrix System: Revision History).
It's believed that he is similar to Neo but nowhere near his power. His limitation is that he can only subtly manipulate information and has no control over gross manipulation.
As the Merovingian's power lies more in subtle rather than gross manipulation of information, he may not be a previous One.