  We present an implementation of the $\mathcal{F}$-statistic to carry out the
first search in data from the Virgo laser interferometric gravitational wave
detector for periodic gravitational waves from a priori unknown, isolated
rotating neutron stars. We searched a frequency $f_0$ range from 100 Hz to 1
kHz and the frequency dependent spindown $f_1$ range from $-1.6\,(f_0/100\,{\rm
Hz}) \times 10^{-9}\,$ Hz/s to zero. A large part of this frequency - spindown
space was unexplored by any of the all-sky searches published so far. Our
method consisted of a coherent search over two-day periods using the
$\mathcal{F}$-statistic, followed by a search for coincidences among the
candidates from the two-day segments. We have introduced a number of novel
techniques and algorithms that allow the use of the Fast Fourier Transform
(FFT) algorithm in the coherent part of the search resulting in a fifty-fold
speed-up in computation of the $\mathcal{F}$-statistic with respect to the
algorithm used in the other pipelines. No significant gravitational wave signal
was found. The sensitivity of the search was estimated by injecting signals
into the data. In the most sensitive parts of the detector band more than 90%
of signals would have been detected with dimensionless gravitational-wave
amplitude greater than $5 \times 10^{-24}$.
