Now do you want the bad news?
It looks like you might have booked your journey segments separately, rather than doing the whole thing on the Eurostar website. I don't know your starting point, so I entered 'Petersfield' (because it's about the same journey time away from Waterloo as you've indicated) and asked the site to plan a journey to Geneva on 1st June. (For the return date I entered 3rd June, assuming a business meeting on the 2nd). That routes you out via the 0855 Eurostar service (leaving Petersfield at 0629) and then onto the DIRECT train from Paris Lyon to Geneva, arriving at 1644. (i.e. a total journey time of 9 HOURS 14 MINUTES. (You can also leave Petersfield at 0746, arriving in Geneva at 1835 =a journey of 9 hours 48 minutes).
The even worse news is that doing everything on the Eurostar website is not only quicker, it's also CHEAPER. (The return fare is £352.00).
OOPS!!!!