Replying to Film speed

so as a hobby for the summer i dug out my mom's ancient fujica st701 35mm camera. it has a last f/1.4 lens that i like but i've only shot a couple of rolls through most of which were sorta tests (the light meter is broken). I've never shot with film before and i was hoping for some knowledge from people who know more than i do. my biggest question is how much of a difference film speed makes. Right now i've been shooting with 400 film and indoors i need to keep the shutter speed slower than 1/30, if i were to use 800 for 1600 speed film would i be able to half and third my shutter speed, respectively, and get the same results?