Train tickets from Zurich to Paris Gare de Lyon

I did your search on the official French rail site
https://en.oui.sncf/en/

and got these results
https://en.oui.sncf/en/results?clientId=a8a672ab-aa85-448c-9ed4-f6d0a40d4a22&language=en&country=EN#!/

If you leave from Basel it is a shorter distance to Paris that would seem to be the only advantage.
Actually it is probably the same route on TGV Lyria that stops in both Basel and Zurich:
Zürich - Basel – Mulhouse – Paris 4 roundtrips per day; travel time 4 h 3 min from Zürich and 3 h 3 min from Basel

Oh yeah and to echo Chris from Basel when you buy the ticket it comes automatically with a seat assignment

I just tried it on the SBB website for 2nd July and it appeared to work, I got as far as it asking for my credit card details. The price was CHF 107.
How far did you get and what error message did you get?
Which train were you trying for (there is one every 2 hours)?
If you got as far as entering your credit card, are you sure your card is authorised for transactions in Switzerland?

You can also try https://www.tgv-lyria.com/en-CH which is the joint Swiss-French company running the trains.

And also do I reserve the seat at the time of ticket purchase or later/earlier??

When you buy a ticket for this train it includes the seat reservation. There is a lot of misunderstanding about reservations, they are only a separate purchase if you have a pass.

whether I take the train from Zurich or Basel...... is there any advantage of one over the other

Depends where you are starting from, is it faster to go XXX - Zürich - Paris or XXX - Basel - Paris?

Actually it is probably the same train the service both Basel and Zurich. Zürich - Basel – Mulhouse – Paris

Jazz, it is the same train. But I have seen posts here where people have read that the train runs from Zürich to Paris and therefore think you have to get on there. From most of the popular places (Luzern, Interlaken) it is quicker to go direct from there to Basel, "cut the corner off" and avoid Zürich.
Again the same advice: Look up the journey you actually want to make (E.g. Luzern to Paris), don't guess "I read somewhere the train starts at Zürich, so I need to buy a ticket Zürich to Paris".

Oh yes.... should’ve mentioned.. I am leaving from Lucerne on that morning. 7.20 am and reaching Zurich by 8.20am. With the train to Paris at 9.20 am I hope this should give me enough time for change of platforms..

Alternatively I can travel from Lucerne to Basel but that ofcourse is a longer travel

Alternatively I can travel from Lucerne to Basel but that ofcourse is a longer travel

No it is actually longer to go Luzern to Zurich to Paris than Luzern to Basel to Paris. It takes 1 hour and 1 to 14 minutes to get from Luzern to Basel SBB. It takes 46 to 54 minutes to get from Luzern to Zurich Hbf. But it takes 1 hour to get from Zurich to Basel on the Paris TGV Lyria, so you save 30 to 45 minutes traveling to Basel and getting it there.

I second what Sam says.
The 09:20 TGV from Zürich stops at Basel, leaving at 10:34. Arrive Paris 13:40.
You can get the 08:30 from Luzern to Basel, arrive 09:45 and connect there. That is nearly an extra hour in bed! Plus 45 minutes at Basel station to buy coffee and lunch to take on the train (10 minutes is enough to change trains at Basel or Zürich).

You can many more details about these TGV trains and how to reserve them here:

www.seat61.com