Ok, it appears that a package has been developed to enhance and simplify the string manipulation toolbox in R (finally!). It is called stringi and looks very promising. Its documentation is very well written, and in particular I find the pages about encodings and locales much more enlightening than some of the standard R documentation on the subject.
It has Unicode normalization functions, as I was looking for (here form C):
> stri_trans_nfc('\u00e9') == stri_trans_nfc('\u0065\u0301')
[1] TRUE
It also contains a smart comparison function which integrates these normalization questions and lessens the pain of having to think about them:
> stri_compare('\u00e9', '\u0065\u0301')
[1] 0
# i.e. equal ;
# otherwise it returns 1 or -1, i.e. greater or lesser, in the alphabetic order.
Thanks to the developers, Marek Gągolewski and Bartek Tartanus, and to Kurt Hornik for the info!