I want to be able to email GAR forms from a tent in France before flying back to the UK.
Sounds like any program that allows you to stick text boxes onto a PDF would suit you just fine, you're not really looking to "edit" as such. The bundled "Preview" program on OS X allows you to do that.... no doubt most from your Google search would too. CutePDF is quite a well known name on Windows.
Anyway, you're after free software, so it'll cost you nothing to download and try.
Having said that, a Google search might even yield a .doc version of the GAR form from one or two Police websites.