Step 1: Oxidation state of cobalt.
In $\mathrm{[CoF_6]^{3-}}$, each fluoride ion has a charge of $-1$.
\[
x + 6(-1) = -3 \Rightarrow x = +3
\]
So, cobalt is in +3 oxidation state.
Step 2: Nature of ligand.
Fluoride ($\mathrm{F^-}$) is a weak field ligand and does not cause pairing of electrons.
Step 3: Hybridisation and geometry.
Due to weak field ligands, outer orbital complex is formed using $sp^3d^2$ hybridisation, resulting in octahedral geometry.
Step 4: Conclusion.
Hence, the correct answer is (B) $sp^3d^2$ and octahedral.