“Moderement anime” means moderately, or somewhat, animated.
Translation: lively-sounding, but slower than presto or allegro molto.
It is entirely possible to play something in an animated way without going as fast as you can. So don’t panic. Making the music sound clear is much more important than playing at top speed. After all, the audience wants to hear the notes!
If the music is staccato, the notes should be short, with a sharp attack and release. The resulting sound would be present, not a dull thud (which would also be appropriate in a different situation).
It might be helpful to think a friend telling you about an event they were excited about. Your friend would be smiling, perhaps gesturing. Their voice would have a lot of ups and downs in pitch, but would not be a whisper. You might ask them to speak more slowly so you can understand them!