Fluorine the element is very reactive, but that doesn't mean its compounds are
Fluorine the gas is a very reactive element because it loves to take electrons from other compounds. But this is irrelevant to whether compounds containing fluorine are reactive. Consider the more common chlorine. Chlorine gas is less reactive than fluorine, but is still very reactive. It is a dangerous and corrosive compound that has been (and probably is still) used as a military weapon. But you encounter very unreactive compounds of chlorine every day. Common salt is a chlorine-containing ionic compound that makes up a significant portion of the electrolytes in your body; PVC is a fairly inert plastic made from a polymer containing chlorine carbon bonds.
The very reactivity of fluorine makes some of its compounds very unreactive. F-C bonds, for example, are very strong and often very unreactive even compared to other carbon-halogen bonds. PTFE (a long carbon chain with all the hydrogens replaced by fluorine) is a very inert polymer that is safe enough to use at the high temperatures achieved in frying pans, for example.
Some fluorine compounds are, however, very biologically active but not because their fluorines are "reactive". Fluoroacetic acid and its salts, for example, are dangerous (and naturally occurring) poisons. But their mechanism of action relies on their stability not their reactivity: they are similar enough to acetic acid that they get involved in the standard citric acid cycle but end up blocking one of the key enzymes to further reactions because the product is too stable.
Whether or not fluorophenibut is "reactive" in the body in the sense you mean is unlikely. It is a neurodepressant similar to gabapentin and pregabalin, though little is known about its safety.
Complicated molecules can't be judged as dangerous, safe or reactive just because of the elements they contain. You need to know the detailed and specific ways they interact with bodily processes. Prozac, for example, is a widely used anti-depressant that contains fluorine. Just because it does doesn't make it reactive or dangerous.