Il suffit de supprimer `and not test {\iffootnote}`
{\iffootnote}` de
\renewbibmacro*{citeindex}{%
\ifboolexpr{ test {\ifciteindex} and not test {\iffootnote} }
{\indexnames{author}}{}}
**MWE**
\documentclass[a4paper,french]{article}
\begin{filecontents}{bib.bib}
@article{Foo2035,
author = {Foop, Beck},
journal = {Journal},
year = {2010},
title = {Title},
doi = {doi},
}
@article{Foo2034,
author = {Foot, Lise},
journal = {Journal},
year = {2010},
title = {Title},
doi = {doi},
}
}\end{filecontents}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{libertine}
\usepackage{textcomp}
\usepackage[backend=biber,
style=apa,
indexing=cite,
sortlocale=fr_FR,
maxnames=15,
]{biblatex}
\DeclareLanguageMapping{french}{french-apa}%La bibliographie est en APA français
\usepackage{apalike}%La bibliographie est en APA
\DefineBibliographyExtras{french}{\restorecommand\mkbibnamelast}% La bibliographie est en français
\addbibresource{bib.bib}
\DeclareUnicodeCharacter{00A0}{ }
\usepackage[babel=true]{csquotes}
\usepackage[makeindex]{splitidx}
\renewbibmacro*{citeindex}{%
\ifboolexpr{ test {\ifciteindex} }
{\indexnames{author}}{}}
\makeindex
\usepackage{babel}
\begin{document}
\cite{Foo2035} pensait aux oiseaux quand il écrivait son livre\footnote{Comme le disait \textcite{Foo2034} les oiseaux sont importants.}
\printbibliography
\printindex
\end{document}
