Set 1,5 line spacing in footnotes

The package setspace makes some work just to avoid footnotes having increased leading.

If you want a devastatingly awful document (I know, it's not your fault, but the institution's rules you have to comply with), then just issue

\linespread{1.5}

before \begin{document} and don't load setspace.

\documentclass[11pt, a4paper, oneside]{book}

\usepackage[hang]{footmisc}
\usepackage{lipsum}

\setlength{\footnotemargin}{2mm}

\linespread{1.5}

\begin{document}

\lipsum*[1]\footnote{\lipsum[1]}

\end{document}

---

By the way, you shouldn't be enclosing the whole document in a spacing environment, but simply issue

\setstretch{1.5}

if you eventually decide to use setspace.

If you're managing this as a one-off thing, you could just use

...\footnote{\setstretch{1.5}...}...

Alternatively, you can add \setstretch{1.5} as part of the \footnotelayout (supplied by the footmisc package):

\renewcommand{\footnotelayout}{\setstretch{1.5}}

Here is an example using the latter suggestion:

\documentclass[11pt, a4paper, oneside]{book}
\usepackage{setspace}
\usepackage[hang]{footmisc}
\usepackage{lipsum}
\renewcommand{\footnotelayout}{\setstretch{1.5}}% Footnotes are \setstretch{1.5}
\setlength{\footnotemargin}{2mm}

\begin{document}

\setstretch{1.5}
\lipsum*[1]\footnote{\lipsum[1]}
\end{document}