There are a number of ways of achieving your goal. The following merely builds on what you've already created:

\documentclass{article}
\usepackage{multido}
\newcommand{\Pointilles}[1]{%
\par\nobreak
\noindent\rule{0pt}{1.5\baselineskip}% Provides a larger gap between the preceding paragraph and the dots
\multido{}{#1}{\noindent\makebox[\linewidth]{\dotfill}\endgraf}% ... dotted lines ...
\bigskip% Gap between dots and next paragraph
}
\begin{document}
Here is some text.
\Pointilles{5}
Here is some more text.
\Pointilles{3}
Here is some final text.
\Pointilles{2}
\end{document}
A minor adjustment to \Pointilles could allow you to stretch the content using an adjustable \strut:

\documentclass{article}
\usepackage{multido}
\newcommand{\Pointilles}[2][3]{%
\par\nobreak
\noindent\rule{0pt}{1.5\baselineskip}% Provides a larger gap between the preceding paragraph and the dots
\multido{}{#2}{\noindent\makebox[\linewidth]{\rule{0pt}{#1\baselineskip}\dotfill}\endgraf}% ... dotted lines ...
\bigskip% Gap between dots and next paragraph
}
\begin{document}
Here is some text.
\Pointilles{5}
Here is some more text.
\Pointilles[1.5]{3}
Here is some final text.
\Pointilles{2}
\end{document}
\documentclass{...}and ending with\end{document}. – Jun 03 '15 at 20:48