You can keep it simple and sincere. In Jain spirit, you do not need to make a big justification.

You could say:

• “I’ve taken a vow for today to avoid secular entertainment, so I won’t be watching a regular movie.”
• “Today is a spiritually observant day for me, so I’m skipping movies and other secular media.”
• “It’s part of my Jain practice today, so I’m not watching films, but I’d still love to spend time with you.”

If you want it to sound warmer and less formal:

• “I’m observing a Jain vow today, so I’m avoiding movies for the day. But I’m happy to hang out in another way.”
• “I can’t watch a movie today because of my religious observance, but let’s do something else together.”

A good Jain way to express it is:

• clear
• non-judgmental
• without criticizing the movie or the other person

If needed, you can also offer an alternative:

• tea
• a walk
• conversation
• a Jain or inspirational talk
• a non-media activity

This keeps your vrat intact while showing vinay and kindness.