There was actually a Festival of Fools parade?!?!?!?! I was only 3
It wasn't a parade, but a "theater in the round" show located at Disneyland in the Big Thunder Ranch area (check YouTube). WDW had a show at the Backlot Theater at Disney-MGM Studios (which was later rebuilt and became the Premiere Theater where they held the SWW events and the first home to the Frozen show). I never saw the Festival of Fools show, but LOVED the Hunchback show at MGM. It used quite a bit of puppetry and was visually stunning. The music was always considered an amazing part of the movie, and the MGM show took full-advantage. It was an example of how movie success and attraction success weren't dependent on each other. Maybe the movie under-performed, but it had successful elements that could be leveraged into a successful attraction.
As for the ways Disney used to synergize their movies. Many of these premiered at the parks the same day the movie premiered, and there were character Meet & Greets as well.
Little Mermaid (1989) - Voyage of the Little Mermaid (open Jan 1992)
Beauty and the Beast (1991) - Stage show at DL and WDW (open Nov 1991); still open at WDW
Aladdin (1992) - Aladdin's Royal Caravan Parade at MGM (Dec 92 - Aug 1995), Disneyland (April 93- May 94)
Lion King (1994) - Lion King Celebration Parade DL (June 94 - June 1997) ; the floats were reused for Festival of the Lion King
Pocahontas (1995) - Spirit of Pocahontas Stage show at DL (June 1995 - Sept 1997) and MGM (June 1995 - Feb 1996)
Hunchback of Notre Dame (1996): Festival of Fools, Show at MGM
Hercules (1997): Parade at DL ( June 1997 - 98); Parade at MGM (June 1997 - spring 1998)
Mulan (1998): Parade at DL (June 1998 - May 1999) & MGM (June 1998 - 1991)
Tarzan (1999): Redo of the Swiss Family Robinson Treehouse at DL (summer 1999 - current); Tarzan Rocks at AK (1999-2006)