The planner is counting that you're coming back to Alicante = 6th travel day. Don't rely on it and count the days yourself.
However I see an issue with your current itinerary. You are limited to 2 days in your country of residence.
The easiest option would be to get a separate Alicante - Barcelona or Barcelona - Lyon ticket in advance, they are relatively cheap.
Pay attention to mandatory reservations in France and Spain (extra costs on top of the pass). They also limit your flexibility as you need to book them in advance on most routes.
Have a look at : https://www.seat61.com/interrail-and-eurail-reservations.htm
Reservations for the Barcelona - Lyon AVE (10€) are only available at RENFE ticket counters. The Paris - Barcelona TGV is also rather expensive (35€), you might prefer to take a domestic TGV to Montpellier or Perpignan and continue on (slow) reservation-free regional trains afterwards.
Questions welcome.
Thank you for your time!! :)