Also interested in some ideas!

For my first English festival I taught food from around the world. I started off showing flags from some of the countries and having them match the flags to the proper country. Then introduced the food. Then played Jeopardy and pictionary (my students LOVE pictionary). I taught that for grades 4 and 5 and then I think my co used it for grade 6 as well.
This English festival I'm doing a song theme for my grade 6 class. I'll show them some English songs (I've been told Justin Bieber and Taylor Swift are popular). Maybe have a worksheet where they fill in missing lyrics. Then put them in groups and have them prepare a performance using one of the songs. They can either sing, rap, act, etc.
However, I'm stuck on my 4th and 5th grade classes for this one. Not sure the song theme is appropriate. Unless I maybe use nursery rhymes and get them to do the actions with the songs?
I've also heard of game show festivals and spelling bee festivals. Maybe those would work?

I'm honestly a little confused; what exactly are English Festivals at your schools? At my school an English festival is a one day performance in the gym. The kids sing English songs or do a skit or something and parents come watch.

I wish! That sounds like so much fun! At my main school the English festival was the kids preparing an English song/dance and performing it for the class.
At my traveling school the English festival can be pretty much anything as long as it's teaching new English vocab. I just finished doing a Disney English festival. It's not really much of a festival. More just a class where we stray from textbook and teach something interesting/fun.

At one of my old schools English Festival was one week and went down something like this:

Daily Pep Rally: 8:00 - 8:30am - English Teachers and student volunteers (usually 5th and 6th graders) stand outside with signs that say things like English is Fun! Good morning! Welcome to the English Festival etc. (The aforementioned students make the signs and they greet other students and try to high five them etc)

Monday: 3rd Grade English Song competition (in pairs or groups)
Tuesday: 4th Grade Spelling Bee
Wednesday: 5th Grade - Role Play Competition - in small groups (costumes, props etc usually made by students)
Thursday:  6th Grade - English Song and Dance Competition (usually done by each class)
Friday: 6th Grade - speech contest (writing and delivering the speech)

Teacher's Role: judging competitions, supervising making signs and dance rehearsal for the 3rd graders, etc