\documentclass[a4paper,12pt]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[margin=1.5cm]{geometry}
\usepackage{tabularx}
\newbox\tabfillbox
\newcommand*\tabfill[2]{%
   \begingroup\parindent0pt
   \ifdim\pagegoal=16383,99999pt \null\par\nointerlineskip\else\ifhmode\par\fi\fi
   \noindent
   \setbox\tabfillbox\vbox{\begin{tabularx}{1\textwidth}{|*{2}{>{\centering\arraybackslash}X|}}\hline
   Colonne A&Colonne B\\\hline\end{tabularx}}%
   \begin{tabularx}{1\textwidth}{|*{2}{>{\centering\arraybackslash}X|}}\hline
   #1&#2\\\hline
   \vrule width0pt height\dimexpr\pagegoal-\pagetotal-\ht\tabfillbox-\dp\tabfillbox depth0pt\relax&\\\hline
   \end{tabularx}\par\endgroup
}
\begin{document}
Ceci est du texte en haut
\[a^2+b^2=c^2\]
et voici le tableau :

\bigskip

\tabfill{Colonne A}{Colonne B}
\end{document}