Presets in the arpeggiator can not be changed via Midi CC or program changes. The workaround is to setup the arp on layer level, then you can use multiple layers using multiple settings/presets which  you can then select via key-switches.

Demonstrated in this video:

Q: I need to have real tremolo. Like a repetition of staccato notes, not a square wave lfo that ups and downs the volume. Is this possible in Falcon? I could of course use an arpeggiator, but this is, my idea, not exactly an elegant solution.

A: If you want actually repeating note-on triggers which trigger the amplitude/filter envelope of each note, there only is the arpeggiator, if you want to modulate the amplitude of a sustained tone, you can draw your own shapes in e.g. a looped multi envelope with multiple segments, or use a ramp down LFO, then you could modulate the modulation depth with another LFO/envelope to make it more organic/less repetitive, and also modulate the speed of the ramp down LFO a little bit with another LFO (like values around 0,02 for modulating LFO speed).