A subbasis $\mathbb S$ for the finite complement topology is the set of all $\mathbb R-x$ where $x \in \mathbb R$. From Munkres I know that the collection of all finite intersections of elements from $\mathbb S$ forms a basis.
Any finite intersection of elements from $\mathbb S$ will be a basis element. That is, any set missing finitely many points will be a basis element. But that is every open set in the finite complement topology, besides $\mathbb R$.
So, is every element from the finite complement topology generated by this subbasis a basis element?