Missing a connection should not lead to extra costs, according to EU legislation. The operator at the station where the connection failed is obliged to propose alternatives or overnight accommodation (if needed) at no extra costs. You can any claim extra costs from the place where you bought your Interrail. Do keep all receipts etc. to be able to prove your extra costs.

Are you in Spain now? A RENFE ticket office should be able to book the train Barcelona - Lyon, as long as there are places available for Interrail. What did the Cordoba and Sevilla stations say? Is the train sold out or did the staff not know how to book this train? Anyway, Interrail reservations for this train are only available on paper, thanks to RENFE and SNCF. You can also try +34 91 232 03 20, which is RENFE's phone sales. You can use it up to 24 hours before departure. You will receive a code which you must use to pick up and pay for your reservation at a local station ticket office, within 72 hours after ordering. Also see:

https://www.interrail.eu/en/plan-your-trip/reservations/how-do-i-book-my-reservations

(under “Spain")

Thank you for your reply.

Renfe Cordoba claimed they had problems to make a reservation. The system was blocked.

Renfe Sevilla claimed there is no station Lyon Part Dieu (!) and they said they couldn't make seat reservations for the international trains. 

Rvdborgt, are you working for Interrail or are you a fellow traveler in this community. I want Interrail to solve my problem. 

Best regards. 

I don't work for Eurail/Interrail, I'm just trying to help and to figure out what is going on. Checking the SNCF booking website, it seems that there are no TGVs running on this route between 10 and 14 November:

So either you go via Portbou (check timetables with the operators, do not rely on the Interrail app) or you'll have to travel on another day.
The Interrail online reservation service does show availibilities up to 9 November or from 15 November. I wouldn't be surprised if the RENFE system just says "not possible” or something similar and the staff don't realise it can mean no trains are running that day.

Edit: there are engineering works in France, so these trains really won't be running on those days.

Hi Jeroen, I am sorry to hear that you have been experiencing issues while travelling. Regarding the train delay, you may be eligible for monetary compensation for the inconvenience caused. Information on our compensation follow and the form to apply for it can be found here. They should be able to issue the reservation but as rvdborgt mentions, they can't as there are no trains running. You either have to go for another route or choose another day to travel. 

@Jeroen Rovers 
Hi:)
Here in this Community are just few Eurail Moderators that overwatch the Group (No Staff from the Customer Service Office) for Cases like yours you have to get in Contact directly with Eurail For example with this Service Form or in case of delays the form mentioned above by Nanja :)