No caption number for figures and tables

You could use \captionsetup from the package caption that way:

\documentclass{article}

\usepackage{caption}

\usepackage{graphicx}

\begin{document}

\begin{figure}[h!]
\centering
\includegraphics[height=2cm]{figure}
\caption{Une figure.}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[height=2cm]{figure1}
\captionsetup{labelformat=empty}
\caption{Une figure.}
\end{figure}

\end{document}

This gives:

You can also use \caption* when using the caption package which keeps only the caption title.

You may do something else what did not work, but this example works as desired:

\documentclass{article}
\usepackage{caption}
\usepackage[demo]{graphicx}
\begin{document}
\begin{figure}[ht]
\centering
\includegraphics{figure1}
\caption*{Caption.}
\end{figure}
\end{document}

I think the simplest way is to enter the caption not enclosed in the caption{} command.

MWE

\documentclass{article}
\usepackage{graphicx}
\begin{document}
\begin{figure}
  \centering
  \includegraphics[width=0.5\textwidth]{Fig_test.png}
  \caption{This with float name and number}
\end{figure}
\begin{figure}
  \centering
  \includegraphics[width=0.5\textwidth]{Fig_test.png}\par
  This with just the caption
\end{figure}
\end{document}