More train strike concern

There is no way to know if the strike will continue. It's already unusual that it has lasted this long.

SNCF is the initials of the French national railroad company, like Amtrak.
TGV is a high-speed train run by the SNCF on long distance rail lines.
RER is a type of metro/subway that goes out to the suburbs. It has a limited number of stops within Paris, mostly at large metro stations. It is not part of the SNCF system, but some of their workers have been on strike, also.

Edit: thanks for the clarifications.

All French trains are operated by SNCF, the French national railway system. TGV is the fastest type they offer and is probably what you're taking for at least part of the first trip (is your ticket direct or with a connection?) and all of the second. RER doesn't apply here; that's the suburban subway system around Paris. Their strike/disruption page in French, allows you to see at least the minimum trains that will be running. You could go ahead and enter your train number there, to see if it's running today, for instance.

If there is a strike on your travel date, your ticket will be good for any train operating that day. Or, once a strike is announced for your travel date, you could exchange the ticket at a French station, but might take more paperwork at a Swiss station (e.g., get a refund later). If you bought tickets online, you can also look at the resources of that web site, such as for Rail Europe: http://ricksteves.raileurope.com/rail-help/.

Actually, a minor correction, the RER is jointly run by both the RATP and SNCF so its is part of the SNCF system. Hence the reason why some RER workers are on strike as well.

Yes, without going into excruciating detail and developing a reputation for pedantry, some of the RER lines are operated exclusively by SNCF staff, and some of the lines are operated by SNCF staff over the outer parts and the inner parts of the lines by RATP. RATP is the operating company of the Métro (and now some TfL (Transport for London) services in London).

Thanks to everyone, I'll keep a close eye as my date of travel approaches and then see if I need to do anything in Geneva.