Requesting information on Paris - Interlaken - Rome Train travel

Hello Friends, I’m travelling solo this November and Paris will be my base. I’ll visit Paris for a few days and then return to the same city at the end to catch my flight back home.

Now, I’m planning to travel to Interlaken to visit Jungfraujoch and the nearby villages and then proceed to Rome for another few days. I have a total of 3 weeks and I believe visiting the aforementioned three places would be easy [earlier I thought I could go to some other city too, like Munich/Barcelona for example]. 

I understand the below is possible but does this plan sound good, or could you please suggest a better idea as this is my first time visiting Europe?

• Take train from Paris to Basel [using 4 days global flxe Eurail pass] and then take local train to Interlaken.
• Purchase single day pass to Jungfraujoch [expensive but I’m not buying Swisspass as I’m just spending 4 days in the country with not many visits to mountain tops or intercity travel].
• Take a local train to a nearby city like Bern/Spiez and change over to a fast train to Rome. Can I reach Rome in a day if I take early trains from these places? 
• Return to Paris from Rome and if I have any spare days, detour via another country, or just go straight to Paris. Are there any direct trains or few changeovers? 

So based on the above plan, would you recommend buying Eurail global flexi pass [4/5 days]? I checked the direct train tickets via Omio or Trainline website but they seem to be close or dearer than the Eurail pass. Am I missing something here to find cheaper tickets? 

Thanks in advance.