editing in 60 FPS

I am working on a Gaming Channel

I will be recording the videos in 120 fps and exporting them out in 60 fps

(Lets use this for example)

however if i buy a template , and that template is lower than 60 fps like 24 or 30 fps. Will that lower my video frame rate down as well. Will I lose that smooth frame rate to the template

Very new to this

Thank you for your help!