The scrlfile package (part of KOMA-Script) features, among other things, a \PreventPackageFromLoading macro that does exactly what its name suggests. You may use it to prevent the ucs and inputenc packages being loaded by europecv. After the class is loaded, we redefine its internal command \ecv@utf so that utf8 really means utf8, lift the ban on package loading and issue \usepackage[uft8]{inputenc}.
\RequirePackage{scrlfile}
\PreventPackageFromLoading{ucs,inputenc}
\documentclass{europecv}
\makeatletter
\renewcommand\ecv@utf[1]{{\inputencoding{utf8}#1}}
\makeatother
\ResetPreventPackageFromLoading
\usepackage[utf8]{inputenc}
\usepackage{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@misc{A01,
author = {Author, A.},
year = {2001},
title = {Alpha},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\nocite{*}
\begin{document}
\printbibliography
\end{document}