Currently on a train from Paris to Lauterbrunnen - Question??

The lack of seat numbers is normal. On Swiss trains, just sit wherever is free. 1st class cars have a yellow band on the outside of the door. When the seat is reserved, there is an indication, but very few people reserve sets. And 1st class is never full (it's the point of 1st class).

I assume you are on the Paris-Basel that arrives at 10:23. This lets you grab coffee or something before the next train to Interlaken Ost leaving from platform 4 at 10:56 (train IC 1069).

At Interlaken Ost, when you change trains again, you will need to sit in the correct half of the train, the one that goes to Lauterbrunnen (it splits halfway). It should all be very clear on the doors. If you see "Grindelwald", you are not in the right car!

EDIT: hold on, your post mentions Geneva. Are you on a train to Geneva or a train to Basel?
If Geneva, which would be strange because it is a longer route, then you need to take a train to Bern first, then Interlaken Ost.

Thank you for your help! We left Paris at 8:16 on a train to Geneve / that connects to Bern - to Interlaken - to Lauterbrunnen… we are actually staying in Murren. I’m still a bit sleepy so there might have been typos in my post - ha!

Ok!
So you should be able to take the 11:42 from Genève to Bern from Platform 4. The final destination is Zürich, don't be fooled by that.
Then, take an onward train to Interlaken. Sometimes, it is faster to first take a train to Spiez, then change for another train to Interlaken.
Download the SBB app to check Swiss train times etc.

Thank you so so much!