Does Fantastical have a URL handler?

Fantastical supports the following URL actions:

x-fantastical3://parse?sentence=[input] — Begin creating a new event with the given sentence. The notes parameter can also be added to specify a note with the event. For example: x-fantastical3://parse?sentence=sentence&notes=[your note]. The following parameters are also supported:

add (set to 1 to automatically add an event - be careful!)
reminder
due (requires the format yyyy-MM-dd HH:mm)
title
location
url
notes
start (requires the format yyyy-MM-dd HH:mm)
end (requires the format yyyy-MM-dd HH:mm)
allDay (can be 1 or 0)
availability (options: free, busy, tentative, unavailable)
private (can be 1 or 0, only applies to Exchange calendars).

Note that if you use the sentence parameter it will cause other parameters to be ignored.

x-fantastical3://show?date=yyyy-mm-dd — Jumps to the specified date. You can also use a natural language date such as "Tuesday" or "next month" and Fantastical will do its best to show the date.

Fantastical supports x-callback-url. x-callback-url can be used by using x-fantastical3://x-callback-url/parse?parameters or x-fantastical3://x-callback-url/show?parameters. The parameters x-source, x-success, x-cancel, and x-error are all supported. Refer to the x-callback-url site for more details.

Fantastical is also officially supported by Launch Center Pro.