I don't think bigfoot package is necessary, you could use
\renewcommand*{\thefootnote}{\fnsymbol{footnote}}
(saving - before - and restoring - after - the numeric value of the footnote counter).
For convenience, I've created two macros (\switchfootnotenumsym and \switchfootnotesymnum) for the switching between the two types of footnotes:
\begin{filecontents}{\jobname.bib}
@Book{author00:_title,
author = {Author},
title = {Title},
publisher = {Publisher},
year = 2000}
\end{filecontents}
\documentclass[12pt,twoside,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english,french]{babel}
\frenchbsetup{StandardLists=true}
\usepackage{setspace}
\usepackage{graphicx}
\usepackage{lmodern}
\usepackage{xspace}
\usepackage{epigraph}
% New counter for switching from numeric footnotes to the ones with symbols and vice-versa
\newcounter{tempfootnote}
% Macro for switching from numeric footnotes to the ones with symbols
\newcommand{\switchfootnotenumsym}{%
\setcounter{tempfootnote}{\value{footnote}} % save the current value of footnote counter
\setcounter{footnote}{0}
\renewcommand*{\thefootnote}{\fnsymbol{footnote}}
}
% Newcommand for switching from the footnote with symbols to the numeric ones
\newcommand{\switchfootnotesymnum}{%
\setcounter{footnote}{\value{tempfootnote}}
\renewcommand{\thefootnote}{\arabic{footnote}}
}
\usepackage{lipsum}
\usepackage{filecontents}
\usepackage[autostyle=true]{csquotes}
\usepackage[style=authoryear-comp,
hyperref,
backend=biber,
isbn=false,
doi=false,
url=false,
date=year]{biblatex}
\AtEveryBibitem{\clearlist{language}}
\renewcommand*{\newunitpunct}{\addcomma\space}
\bibliography{\jobname}
\usepackage[colorlinks]{hyperref}
\begin{document}
\switchfootnotenumsym
\setcounter{footnote}{1}% if you want the \dagger (which is the number two) set the counter to one
\epigraph{Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut}{Author\footnotemark}
\footcitetext{author00:_title}
\switchfootnotesymnum
Normal text\footnote{Normal footnote}
\switchfootnotenumsym
This is only to show you the correspondence between numbers and symbols (they are only 9):
1\footnote{footnote} 2\footnote{footnote} 3\footnote{footnote} 4\footnote{footnote} 5\footnote{footnote}
6\footnote{footnote} 7\footnote{footnote} 8\footnote{footnote} 9\footnote{footnote}
\switchfootnotesymnum
Other normal text\footnote{With other normal footnote}
\end{document}

Credits to Stefan Kottwitz.
Edit:
If you need a continuing symbol footnote counter (remember that the symbols are only 9, you will get an error if the symbol footnote counter becomes > 9):
\begin{filecontents}{\jobname.bib}
@Book{author00:_title,
author = {Author},
title = {Title},
publisher = {Publisher},
year = 2000}
\end{filecontents}
\documentclass[12pt,twoside,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english,french]{babel}
\frenchbsetup{StandardLists=true}
\usepackage{setspace}
\usepackage{graphicx}
\usepackage{lmodern}
\usepackage{xspace}
\usepackage{epigraph}
% New counters for switching from numeric footnotes to the ones with symbols and vice-versa
\newcounter{tempfootnotenum}
\newcounter{tempfootnotesym}
\setcounter{tempfootnotenum}{0}% initial value
\setcounter{tempfootnotesym}{0}% initial value
% Macro for switching from numeric footnotes to the ones with symbols
\newcommand{\switchfootnotenumsym}{%
\setcounter{tempfootnotenum}{\value{footnote}}% save the current value of numeric footnote counter
\setcounter{footnote}{\value{tempfootnotesym}}% restore the value of the previous symbol footnote counter
\renewcommand*{\thefootnote}{\fnsymbol{footnote}}% set footnote with symbols
}
% Newcommand for switching from the footnote with symbols to the numeric ones
\newcommand{\switchfootnotesymnum}{%
\setcounter{tempfootnotesym}{\value{footnote}}% save the current value of symbol footnote counter
\setcounter{footnote}{\value{tempfootnotenum}}% restore the value of the previous numeric footnote counter
\renewcommand{\thefootnote}{\arabic{footnote}}% set numeric footnote
}
\usepackage{lipsum}
\usepackage{filecontents}
\usepackage[autostyle=true]{csquotes}
\usepackage[style=authoryear-comp,
hyperref,
backend=biber,
isbn=false,
doi=false,
url=false,
date=year]{biblatex}
\AtEveryBibitem{\clearlist{language}}
\renewcommand*{\newunitpunct}{\addcomma\space}
\bibliography{\jobname}
\usepackage[colorlinks]{hyperref}
\begin{document}
\switchfootnotenumsym
\epigraph{Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut}{Author\footnotemark}
\footcitetext{author00:_title}
\switchfootnotesymnum
Normal text\footnote{Normal footnote}
\switchfootnotenumsym
\epigraph{We love ducks}{Author\footnotemark}
\footcitetext{author00:_title}
\switchfootnotesymnum
Other normal text\footnote{With another normal footnote}
\switchfootnotenumsym
\epigraph{We love lions, too}{Author\footnotemark}
\footcitetext{author00:_title}
\switchfootnotesymnum
I hope this is what you need\footnote{Third footnote}
\end{document}

\setcounter{footnote}{}for symbols as well. [An aside: the answer is really super, but there are lot of info there, in the sense that for somebody that is not supergood at LaTeX – like me... ;D – it can be a bit overwhelming, and it can become very difficult to extrapolate the relevant info.] – Kolmin Apr 20 '17 at 21:22\renewcommandto get symbols, then I had to use\setcounterto pick the desired symbol (something I really didn't conceive at all – shame on me!), and finally I had to use\renewcommandto go back to numbers. – Kolmin Apr 21 '17 at 08:19