pre-subscript alignment with tensor package

No package needed (here I load amsmath because any document with mathematics should).

\documentclass{article}
\usepackage{amsmath}

\newcommand{\hypgeo}[2]{%
  {\vphantom{F}}_{#1}\kern-\scriptspace F_{#2}%
}

\begin{document}

$\hypgeo{2}{3}$

$3\,\hypgeo{2}{3}$

\end{document}

Note the removal of \scriptspace to move the prescript next to the F. A thin space should be inserted between a factor and the hypergeometric function symbol.

This insertion can be made automatic by making the symbol into an operator (and here amsmath has a role):

\documentclass{article}
\usepackage{amsmath}

\newcommand{\hypgeo}[2]{%
  \operatorname{%
    {\vphantom{\mathnormal{F}}}_{#1}%
    \kern-\scriptspace
    \mathnormal{F}_{#2}%
  }%
}

\begin{document}

$\hypgeo{2}{3}$

$3\hypgeo{2}{3}$

\end{document}