BoBD, ATC speak English (although we could start a debate about the quality thereof on the Spanish side
), however in La Juliana it's mainly Spanish, unless there is a certain UK meatbombing operation active. That said, LEJU is non-towered, so you actually talk to Seville for ATC and on the local frequency for LEJU traffic.
Deeday, Badajoz is military with only two slots for GA movement available per day (either side of scheduled Iberia arrivals/departures). There may be exceptions in place for people based there, otherwise this is not a very straightforward proposition (plus it's very far from the location of the OP).
I've never rented in Portugal, but there seems to be a pretty active GA scene there (and - contrary to Spain - good command of English is pretty widespread), so you should be ok.