The effective covalent atomic radius is defined as one half of the distance between two nuclei of the element that are held together by a single covalent bond. [H B Grey, Chemical Bonds: An Introduction to Atomic and Molecular Structure, Chapter 2]. read more
Neon is mono atomic whereas fluorine is a diatomic molecule. so what we find as the atomic radius of a noble gas is its van der waal radius and not its covalent radius. whereas for a fluorine molecule we measure its covalent radius. read more
It is true that atomic radius decreases across the period however, neon being an inert gas experiences more repulsion between the the different shells of electrons thus increases the size so much that it is even bigger than the first element in the period. read more
Now when i want to answer why atomic radius of neon is greater than that of fluorine it is because neon is a noble gas or inert gas it has van der Waals radii and due to the reason given above it is greater than that of fluorine. BTW fluorine has covalent radius which is obviously smaller than van der Waals radii. read more