I am planning to be in Barcelona for 6 days. This is my first time being in Barcelona, first time in Europe. I have been reading a lot of what to do and see. I am looking for suggestion for day trips or sites to see. I was even thinking about doing a day trip to southern France if time allows.

6 days will give you enough time to explore the city and the surrounding area, It will all depend on what you want to see amd do.

Is that 6 full days, excluding travel time to/from Barcelona?

Stay in Barcelona. There's more than enough to do there and in the surrounding area.

One of the major rookie mistakes is to try to cram too much into a vacation trip. They end up spending too much time traveling and don't see or experience much.

As my mother says on her tours, with one day here and one day there, with everyone getting on the bus "we saw everything, sort of".

One of the most cutting edge flamenco festivals in the country goes on in Barcelona from Wed 22 to Sat 25 of May. The Ciuatat flamenco/flamenco city festival is up in the Mercat de les Flors theater in the Montjuic hights with spectacular views of the city.

Although flamenco comes from the South, there's a great flamenco culture in Barcelona, quite the contrary to what most tourists think. Many of the greatest artist on the current scene comes from the area, and this festival attracts the very best. http://www.mercatflors.cat/es/ciclo/ciudad-flamenco/

I suggest visiting Girona as a daytrip from Barcelona. It's one hour by train. A lovely city. You won't be disappointed. You have enough time. We spent 5 full days in Barcelona & then went on a 3-day roadtrip, which included 2 nights in Girona. But it is entirely possible to visit Girona in one day as a day trip from Barcelona.

We're in the city next week and plan to visit Montserrat, returning via San Sadurni d'Anoia and my favourite Cava house.

Depending on what you like to do, it is very easy to fill six days in Barcelona. There are excellent museums, the seafront, Gaudi and other buildings and endless opportunities to wander around, sit at cafes and enjoy life.

Getting to southern France is a grind, even with the new high-speed rail link from Figueres. It's definitely not a day trip. We went to Montserrat in May and that was worthwhile. You can take the train or rent a car, which allows for some sightseeing on the way.

Sitges and/or Tarragona are good day trips, again by train or car.

I love Barcelona but there are a lot of things in Barcelona I'm not much interested in also.

I think one day and that is all might be set aside for a trip outside of the city.

You do not mention your interests so it is hard to advise about "all the things" because you may not be the least bit interested in some of them.