International? That's a great idea but I think R6 has a very limited capacity to store records outside UK.
The tools available (and I do hope someone will correct me here, I'd be delighted to learn of something else) are at GBIF where I think the best you can do as regards recording is to download their spreadsheet. To obtain European species lists you'd have to work with the EDIT taxonomic editor (which is listed on the GBIF site) but I honestly cannot recommend spending any effort on it unless you find someone who has already worked on your subject area. Fauna Europaea also has a spreadsheet but I think theirs was basically a fixed-term initiative (I'm still trying to work out their story).
Maps are going to be your downfall as regards European work but if you obtain QGIS and use the TDWG geospatial data (definitive country outlines) then you've got something that will enable you to plot European occurrences (eventually.)
Is there any European funding to turn R6 into a Europe-wide application?