The tendency of an atom to attract a shared pair of electrons towards itself 'is called electronegativity. The smaller the atom, the closer will be the last valence shell from the nucleus, and hence greater the nuclear pull.
Atomic size:
If we down the group, the number of shells increases, hence the size increases.
Now both Fluorine and Chlorine belong to group 17 of the periodic table, the atomic number of Fluorine is while for chlorine it is . Thus, Fluorine comes before Chlorine .
This means Fluorine has a smaller atomic size than Chlorine, which implies that it is more electronegative than Chlorine.
The tendency to accept an electron to get a stable valence shell configuration in Fluorine is higher than that of Chlorine, which makes Fluorine more reactive.