I finally got the solution, here's what I did :
-
based on the comments of this person, I uninstalled MikTeX and the complete TeX distributions on my computer. Since I use Ubuntu, I used
purge
to remove MikTeX, TeXLive, tex-commons, etc. -
then, I installed (or re-installed) TinyTeX (details here)
-
I installed manually the packages I needed with
tlmgr_install()
. Normally, it can be done automatically but that's what I did. -
finally, I replaced
biber
bybibtex
in\usepackage[backend = biber]{biblatex}
(this person explains why it is important)
This last step made it work, but I don't know if the previous ones are important or not. Since he succeeded in compiling the bibliography too, I suppose it is necessary but there's no way for me to prove it.
Anyway, now, when I compile the Sweave document, the bibliography is directly created. Thanks a lot to this person for his/her ideas.
Edit : I re-installed MikTeX after all of this and it works too.