Control vertical space between answers in alterqcm

Werner's answer is fine. Alterqcm uses a tabular and in the last version, I added a longtable option. In fact some problems arrive because one question or one proposition takes a lot of space. The good way is to use a global method like the FACTOR approach or like the LENGTH approach and then you can use a local approach.

You can modify the position of the questions with pq=..., the questions are moved inside the case. The modifications are global with \begin{alterqcm}[lq=85mm,pq=2mm]and local with \AQquestion[pq=6mm]{...}.

If you want more space for a one proposition, you can add something like \AQms(16,14). This a rule with no width ( a phantom ) and it's often very useful to put the proposition inside a minipage to get a correct result.

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[upright]{fourier}
\usepackage{alterqcm}

\parindent0pt
\begin{document}
\begin{alterqcm}[lq=8cm,language=english,pq=-6mm] 
 \AQquestion{Question}{% 
 {Proposition 1},
 {Proposition 2},
 {Proposition 3}} 
\AQquestion[pq=0mm]{Question}{% 
 {Proposition 1},
 {\AQms(16,14) Proposition 2},
 {Proposition 3}}   
\end{alterqcm}

\end{document} 

Update with fractions. The first array is correct but if you use \arraystretchyou need to add pq=- ...to get a correct placement.

\documentclass[a4paper,10pt]{article} 
\usepackage[utf8]{inputenc}
\usepackage{fourier}
\usepackage{amsmath,alterqcm}     

\begin{document}  

    \begin{alterqcm}[lq=85mm]
    \AQquestion{Pour tout réel $x$, le nombre \[\dfrac{\text{e}^x - 1}{\text{e}^x + 2}\hskip12pt \text{égal à :} \] }
    {{$-\dfrac{1}{2}$},
    {$\dfrac{\text{e}^{-x} - 1}{\text{e}^{-x} + 2}$},
    {$\dfrac{1 - \text{e}^{-x}}{1 + 2\text{e}^{-x}}$}
    }
    \AQquestion{On pose I $= \displaystyle\int_{\ln 2}^{\ln 3} \dfrac{1}{\text{e}^x - 1}\,\text{d}x$ et J $ = \displaystyle\int_{\ln 2}^{\ln 3} \dfrac{\text{e}^x}{\text{e}^x - 1}\,\text{d}x$ \\ alors le nombre  I $-$ J est égal à}
    {{$\ln \dfrac{2}{3}$},
    {$\ln \dfrac{3}{2}$},
    {$\dfrac{3}{2}$}
    }
    \end{alterqcm}  

    {\renewcommand{\arraystretch}{2}
        \begin{alterqcm}[lq=85mm,pq=-4mm]
    \AQquestion{Pour tout réel $x$, le nombre \[\dfrac{\text{e}^x - 1}{\text{e}^x + 2}\hskip12pt \text{égal à :} \] }
    {{$-\dfrac{1}{2}$},
    {$\dfrac{\text{e}^{-x} - 1}{\text{e}^{-x} + 2}$},
    {$\dfrac{1 - \text{e}^{-x}}{1 + 2\text{e}^{-x}}$}
    }
    \AQquestion{On pose I $= \displaystyle\int_{\ln 2}^{\ln 3} \dfrac{1}{\text{e}^x - 1}\,\text{d}x$ et J $ = \displaystyle\int_{\ln 2}^{\ln 3} \dfrac{\text{e}^x}{\text{e}^x - 1}\,\text{d}x$ \\ alors le nombre  I $-$ J est égal à}
    {{$\ln \dfrac{2}{3}$},
    {$\ln \dfrac{3}{2}$},
    {$\dfrac{3}{2}$}
    }
\end{alterqcm} }

\end{document}

Since the typesetting of the alterqcm environment is done in a tabular, you can perform the same adjustments you normally would for gaining extra row height. Here's a minimal example:

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[upright]{fourier}
\usepackage{alterqcm}

\setlength{\parindent}{0pt}
\begin{document}
\begin{alterqcm}[lq=8cm,language=english] 
 \AQquestion{Question}{% 
 {Proposition 1},
 {Proposition 2},
 {Proposition 3}}  
\end{alterqcm}

\bigskip

% =========== FACTOR approach ===========
{\renewcommand{\arraystretch}{2}
\begin{alterqcm}[lq=8cm,language=english] 
 \AQquestion{Question}{% 
 {Proposition 1},
 {Proposition 2},
 {Proposition 3}}  
\end{alterqcm}}

\bigskip

% =========== LENGTH approach ===========
{\setlength{\extrarowheight}{20pt}%
\begin{alterqcm}[lq=8cm,language=english] 
 \AQquestion{Question}{% 
 {Proposition 1},
 {Proposition 2},
 {Proposition 3}}  
\end{alterqcm}}

\end{document}

Although I've enlarged the vertical spacing, you can specify a fraction for \arraystretch or negative lengths for \extrarowheight.

This controls global changes for the entire alterqcm environment (header and body).