Yes some Companies charge ontop of the Railpass fee´s for Reservation or even a Railpassuser surcharge (Most of them in Spain,France,Italy)
SNCF (French Rail) made it this year even harder to reserve as they stoped to sell reservations online or by phone 
In case of the International TGV from Barcelona to Paris you could try your luck by Belgian Rail (B-Europe) or German Rail (DB)
You can often avoid the expensive ones by useing slower trains and maybe few more changes on the way.
International TGV´s and Thalys are the most expensive examples :/
Barcelona - Paris you could go with Regionaltrains via Portbou/Cerbere and catch then in Perpignan a domestic TGV (10€/20€) to Paris
Paris - Amsterdam similar as above domestic TGV (10€/20€) to Lille and from there with Belgian and Dutch Intercities reservation free to Amsterdam
Amsterdam - Berlin no reservation needed but often recommened can be done online for 4€ directly on bahn.de without any service fee :)
Berlin - Rome depends on which Route you take 
easiest way afternoon ICE to Munich and from there with the direct Nighttrain to Rome. Only the Nighttrain needs a reservation starting from 14€ for a seat and up to 150€ for private Sleeper cabin with private shower/WC
Hi Seewulf! Thanks for your quick help
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I see, I understand now, I’ll have to pay if I want to go on that train from Barcelona to Paris.
The problem now is, as you say, that I can only book one tram (the one from Barcelona (Sants) to Perpignan (France) in Renfe SNCF, but then it doesn’t allow me to book the second part from Perpignan to Paris in TGV. It says “We couldn’t find any prices results for this connection. Search again or try to find another way to book”.
What do they mean with “another way to book”? (I cannot do it in person since I’m not physically in Europe..)
Regarding your suggention to book in other pages, I have a doubt: I thought that since I bought the Global Pass from Eurail, I must book here in their platform. Can I book in the trains companies own platforms online and still use my Global Pass?
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Thank you again!! 
This is so hard for first time travellers…
Ailin
I get that you have to make seat reservations to guarantee seats! However, I am finding that the seat reservation (for my trips) cost as much as the Global Pass I bought. For example, I bought a 15-day Global Pass for $1,200.00 for two people. Seat reservations from Barcelona - London - Frankfurt - Barcelona is $485 (for two people). Do I really have to pay that much more? So, what is the Global Pass for?
Yes-we (that means a few very experienced long time train users who know many tricks and even take the time to share this with those who ask, NOT the only positive PR talking pass sellers) warn for this all the time but nonetheless all newbees seem to want to ride exactly just those trains that are so expensive in supplement. Go somewhere else-EUR is big enough for many more exciting places or bite the bullet. Or-as has also been suggested-forget that pass and tie yourself in to fix booked advance tickets-with a big chance after 3-4 monthes the covid makes all things have changed by then.
A cheap flight Ams-Barca cost around 30/40 eur-thats less as what the always so happy to strike French railways want for only the supplement for a shorter ride.
Most newbees cannot think of anything else as visiting the capitals with a direct train ride in between.
SO; IF you choose f.e. AMSterdam-Berlin-Praha-Bratislava or Wien (Vienna for you)-Budapest-Ljubljana (ever heard of it? quite a nice small town)-Venezia (not a capital, but quite famous)-then you do not even need (but can if wanted-for an odd eur or so) any REServations. Direct trains-on most every hour or 2 hours and easy daytravel.
