Substitute for eqnarray?

You have to understand that in align and similar amsmath environments, if you want n alignment groups, each group except the first requires 2 ampersands: the first & introduces a new alignment group, and the second & specifies the alignment point inside this group. The first group doesn't require the first ampersand, of course, so n alignment groups in all require 2 n – 1 &s.

You have used the eqnarray syntax, with two &, so amsmath understands there are two groups. As there's no & for the alignment point in the second group, it is aligned on the last characters of each line.

Added:

An easy solution to your problem is obtained with the eqparbox package. Incidentally, I simplified your code for geometry (since all your margins are equal you can simply set margin =). Also, the frenchb option is ibsolete, and should be replaced with french, preferable loaded with the \documentclass, so that all language-dependent packages be informed. Lastn needless to load amsfonts, since amssymb does it for you.

\documentclass[12pt, french]{article}
\usepackage{amsmath,amssymb} % Tableaux, maths
\usepackage{babel}
\usepackage[margin=1.5cm]{geometry} % Marges
\usepackage{eqparbox}
\newcommand{\eqrel}[2][B]{\mathrel{\eqmakebox[#1]{#2}}} %% eqparbox uses a system of tags, which is the optional argument here – defaults to B.

\begin{document}

\begin{align*}
  \emph{Test~align*} &\eqrel{$=$} \text{Bad alignment} \\
  &\eqrel{\em Because} \text{the text is left-aligned, near the equal sign}
\end{align*}

\end{document} 

in align you have one ampersand to much:

\documentclass[12pt]{article}
\usepackage{amsmath,amsfonts,amssymb} % Tableaux, maths
\usepackage[frenchb]{babel}
\usepackage[top=1.5cm,bottom=1.5cm,right=1.5cm,left=1.5cm]{geometry} % Marges
\begin{document}
\begin{align*}
  Test~align*   & = \text{Bad alignment} \\
  Because       & = \text{the text is right-aligned, far to the equal sign}
\end{align*}
or 
\begin{align*}
  Test~align*   & = \text{Bad alignment} \\
                & \text{Because the text is right-aligned, far to the equal sign}
\end{align*}
or 
\begin{align*}
  Test~align*   & = \parbox[t]{0.4\linewidth}{
                    Bad alignment \\
                    Because the text is right-aligned, far to the equal sign}
\end{align*}
\end{document}

adedndum: apparently you looking for the following:

\documentclass[12pt]{article}
\usepackage{amsmath} 

\begin{document}
\[\setlength\arraycolsep{2pt}
\begin{array}{rcl}
  Test~array    & =         & \text{Fine alignment}\\
                & Because   & \text{the text is left-aligned \dots}
\end{array}
\]
\end{document}

addendum (2): with help of very old (and almost forgotten) package mathenv from mfwtools:

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{mathenv}
\usepackage[frenchb]{babel}
\usepackage[top=1.5cm,bottom=1.5cm,right=1.5cm,left=1.5cm]{geometry} % Marges

\begin{document}
\begin{eqnarray}[rc@{\;}l]
  Test~eqnarray &   =     & \text{Good alignment} \\
                & Because & \text{the text is aligned near to the equal sign}
\end{eqnarray}
\end{document}