The electron gain enthalpy of fluorine is ___________.

When an electron is added to the atom the electron gain enthalpy is negative. The more negative the electron gain enthalpy of an element greater the tendency of its atom to accept an electron and the more stable the anion that results. 

As fluorine contains already 7 electrons in the outermost valence shell, so it requires only one electron to complete its octet. So, it easily accepts one electron to form an anion. Hence, energy is released in the process and the electro-gain enthalpy of fluorine is negative.