Trains - Passes - Transfers - Is Eurail right for us?

For these trips it's not really worth to get a pass, and many local public transport routes aren't even covered by the pass. The pass really mostly covers trains, which in Europe can be used for longer distances.

A ticket for the tube/Elisabeth line costs about £13. Not worth to use your pass, and the pass does not cover the tube anyway.

The only long distance train you seem to be taking. You're probably cheaper of buying a ticket directly with eurostar.com for the day you need it, instead of buying a pass and the necessary €34-reservation for Eurostar.

RER is not covered by Eurail. Tickets cost about €10 iirc.

Use local public transport or a shuttle service. 

Metro and Aerobús are not covered by Eurail. Rodalies is but is fairly impractical from T1 and otherwise also cheap (~€5), so a waste to use a pass for this.

You could use a pass to get from Paris to Barcelona, a 6h40 journey by TGV high speed train. You'd need a €35 seat reservation for that on top of your pass but it's pretty scenic. You could also buy a separate ticket for this, probably better as a pass is still probably not worth it.

Overall, don't think an Eurail pass is suited for your trip. It is in general not worth it just for airport transfers (only very few are covered and these don't exceed €15 per trip)

Schelte, thank you so much for the detailed response. I had a feeling this was the case. But good to hear it direct from people that have real life experience. Keeping it simple sounds fine to me.