Oh no, I strongly suggest you don't do that.
Unless you plan to wear a hot pink shirt and Winsor yellow trousers to go with (I'm kidding), red is a very sharp color and needs to be toned down, which is mostly done with a jacket (full suit that is). But in this case assuming this isn't a Christmas related event nor is too formal, things are different
They key tip for formal wear is, that every component should compliment one another.
It doesn't have to match as such, but it should look cohesive. Just like how your shoes match you belt (this is not a rule, but it is traditionally done). Tie and socks also look good when matched.
You can never go wrong with a crisp white dress shirt, black trousers (they may be slightly textured or/and have very subtle grid pattern or lines etc), a silk slim-tie and black shoes. Don't be reluctant to spend on quality if you have to, because these are the essential items of your wardrobe, and they are really worth the price.
If you want to be a little adventurous, I suggest you experiment with the trousers, choose sapphire/royal blue. Try your best to keep the tie black, they look best best in that color. You can also use that same tie for the rest of your life and it would always look perfect, with every formal outfit.
Keep the shirt in lighter colors since you are wearing a tie and not going with a suit. If not white, any pastel color would do, but prefer cream, beige and gray hues. Gray looks wonderful with a tie.
If your event is casual-formal, then you can even play around with the trouser even more. even checked trousers like this
would do. But this is usually a summers look so if you go with this, make sure the pattern is very very subtle.
In belts, go for a very simple, decent one with no fancy buckles or stuff. You can do black or chocolate brown but try to stick two either of these two and keep it leather. Again, its suggested it matches your shoes.
Lastly given that you do insist on the red tie, go with a brown belt (VERRY simple brass-bronze buckle), white dress shirt and black pants. And yes, silk shirts or silk trousers are a big NO NO NO. So are white leather shoes. Totally out of fashion and look tacky when experimented with.
Don't be reluctant to spend a little more if you have to, it REALLY pays off. These things will come handy in the long run, and simpler, the better. Make sure you have a great not-too-loud fragrance, everything should be nicely ironed, try to drop cuff-lings unless others are doing it. Your hair should be freshly cut and washed up whenever you wear formal, you should be properly shaved.
Sorry if this was too long, but I really spend my time on clothing questions, and especially the formal attire ones, because good taste in dressing (for me), sets apart the gentlemen from those who aren't. I am glad you took the concern of asking for suggestions. Good luck!