While Star Fox 64 (VC) does save some things (high scores, stage medals, ect.)... It does NOT have any traditional save support (no save slots whatsoever).
The main reason here is that Star Fox 64 is considered too short as it's an "on rails" shooter (with a few free roam areas). You play 7 stages with limited lives & branching paths, so you can't see everything in one run (you typically need to play 3 times to go through all the levels at least once). You can do multiple play-thoughs in one sitting, so you don't need to save your game.
Having that said, all Wii U VC titles have a "Restore Point" slot within the Virtual Console service... so you can save your spot (outside the game itself), if you absolutely need it. However, gaming purists probably won't utilize it.