The problem here is that you selected the Babel option ngerman, and fancyref only supports german and english. It hasn’t been updated since last century, so it doesn’t know about Neue Rechtschreibung.
You could use a more recent package such as cleveref, or perhaps hyperref together with varioref. Here is the same document rewritten to use cleveref (with a search-and-replace for \fref and \cref).
\documentclass[
fontsize=11pt,
paper=a4,
DIV=10,
BCOR=8mm,
oneside,
english,
ngerman]{scrreprt}
\usepackage{blindtext}
\usepackage{babel,cleveref}
\begin{document}
\chapter{Chapter 1}
\blindtext
Test of \cref{eq:reaction1} and of \cref{tab:table1}.
\begin{equation}
A
\label{eq:reaction1}
\end{equation}
\begin{table}
\centering
\caption{One}
\begin{tabular}{cc}
1 & 2 \\
3 & 4 \\
\end{tabular}
\label{tab:table1}
\end{table}
\selectlanguage{english}
\chapter{Chapter 2}
\begin{table}
\centering
\caption{Two}
\begin{tabular}{cc}
1 & 2 \\
3 & 4 \\
\end{tabular}
\label{tab:table2}
\end{table}
Test of reference with \cref{eq:reaction1} and \cref{tab:table2}.
\end{document}
If you want to stay loyal to fancyref, you could change ngerman to german. Another temporary workaround is to copy the code to create new Babel “captions” from german to ngerman.
\documentclass[fontsize=11pt, paper=a4, DIV=10, BCOR=8mm, oneside]{scrreprt}
\usepackage{blindtext}
\usepackage[english,ngerman]{babel}
\usepackage[english,german]{fancyref}
\fancyrefaddcaptions{ngerman}{%
\providecommand*{\chaptername}{Kapitel}%
\providecommand*{\figurename}{Abbildung}%
\providecommand*{\pagename}{Seite}%
\providecommand*{\tablename}{Tabelle}%
\renewcommand*{\Frefchapname}{\chaptername}%
\renewcommand*{\Frefenumname}{Punkt}%
\renewcommand*{\Frefeqname}{Gleichung}%
\renewcommand*{\Freffigname}{\figurename}%
\renewcommand*{\Freffigshortname}{Abb.}%
\renewcommand*{\Freffnname}{Fu\ss note}%
\renewcommand*{\Frefonname}{Auf}%
\renewcommand*{\Frefpgname}{\pagename}%
\renewcommand*{\Frefpgshortname}{S.}%
\renewcommand*{\Frefsecname}{Abschnitt}%
\renewcommand*{\Frefseename}{Siehe}%
\renewcommand*{\Freftabname}{\tablename}%
\renewcommand*{\Freftabshortname}{Tab.}%
\renewcommand*{\frefchapname}{\Frefchapname}%
\renewcommand*{\frefenumname}{\Frefenumname}%
\renewcommand*{\frefeqname}{\Frefeqname}%
\renewcommand*{\freffigname}{\Freffigname}%
\renewcommand*{\freffigshortname}{\Freffigshortname}%
\renewcommand*{\freffnname}{\Freffnname}%
\renewcommand*{\frefonname}{%
\MakeLowercase{\Frefonname}%
}%
\renewcommand*{\frefpgname}{\Frefpgname}%
\renewcommand*{\frefpgshortname}{\Frefpgshortname}%
\renewcommand*{\frefsecname}{\Frefsecname}%
\renewcommand*{\frefseename}{%
\MakeLowercase{\Frefseename}%
}%
\renewcommand*{\freftabname}{\Freftabname}%
\renewcommand*{\freftabshortname}{\Freftabshortname}%
}%
\begin{document}
\chapter{Chapter 1}
\blindtext
Test of \fref{eq:reaction1} and of \fref{tab:table1}.
\begin{equation}
A
\label{eq:reaction1}
\end{equation}
\begin{table}
\centering
\caption{One}
\begin{tabular}{cc}
1 & 2 \\
3 & 4 \\
\end{tabular}
\label{tab:table1}
\end{table}
\selectlanguage{english}
\chapter{Chapter 2}
\begin{table}
\centering
\caption{Two}
\begin{tabular}{cc}
1 & 2 \\
3 & 4 \\
\end{tabular}
\label{tab:table2}
\end{table}
Test of reference with \fref{eq:reaction1} and \fref{tab:table2}.
\end{document}
Monkey-patching is far from an ideal solution, since if the package ever did get an update, this code would still depend on the version from the 1990s.
