How to change the color of the short version of the acronym in the list of acronym

With your current settings, the List of Acronyms is typeset using a description environment, so you can change \descriptionlabel for the acronym environment using, for example:

\usepackage{etoolbox}
\AtBeginEnvironment{acronym}{%
  \renewcommand*\descriptionlabel[1]{\hspace\labelsep
                                \normalfont\bfseries\color{blue} #1}}

A complete example:

\documentclass[12pt,a4paper,english,french]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8x]{inputenc}
\usepackage[frenchb]{babel}
\usepackage{lmodern}
\usepackage{xcolor}
\usepackage{setspace}
\usepackage{etoolbox}
\usepackage[withpage]{acronym}
\usepackage[colorlinks=true, linkcolor=blue]{hyperref}
\hypersetup{colorlinks=true,citecolor=blue} 

\AtBeginEnvironment{acronym}{%
  \renewcommand*\descriptionlabel[1]{\hspace\labelsep
                                \normalfont\bfseries\color{blue} #1}}

\title{My Thesis Document}
\begin{document}
\maketitle
\newpage
{\setlength{\baselineskip}{1.2\baselineskip} 
\tableofcontents\par}
\hrule
\vspace{1cm}
\section*{List of Acronyms}  
\begin{acronym} \renewcommand{\\}{}  
\acro{TTC}{Tunisiano Tourism Company} % <---- Make TTC in blue for example
\acro{CBT}{Central Bank of Tunisia}
% etc
\end{acronym}
\newpage
\begin{spacing}{1.5}
\section{First Section}
Text about the \ac{TTC}, etc
\section{Second Section}
Text about the \ac{CBT}, etc
\end{spacing}
\end{document}

If you were using the optional argument for acronym with a value different than 1, then one simply would have to change \bflabel

\def\bflabel#1{{\textbf{\textsf{\color{blue}#1}}\hfill}}