I would pick March, because it starts to get pretty warm by April. If you're religious, try to plan around Easter. Some churches may not like having a wedding during lent... You'll miss the parades, they're in February. Any other tips, we got married in Baton Rouge last year and I LOVE MY FLORIST if you haven't picked one yet. Flowers by Jimmy Thomas. His work is AMAZING, the website doesn't show half the stuff he can do! 2836 government St, Baton Rouge, LA 70806 (225) 344-4361 (800) 960-4361. http://www.flowersbyjimmythomas.com/
I agree. March is a great month in Baton Rouge. It rains quite a bit in March though. Many outdoor events start in the month of April because of the nicer (sunnier) weather - Fest For All, Live After Five, etc. I also agree that Flowers by Jimmy Thomas is great. I did not use him as my florist, but I have been to many events with flowers by him and they are always so very beautiful.
I second the other girls on the florist - I'm using Bloom, Inc. (formerly known as Flowers by Jimmy Thomas). Casey Johnson is the new owner and he is awesome. His style is very modern, and his prices are great. Definitely give him a call! As for the months, I think you'll be fine with either March or April. The weather is usually perfect that time of year (it starts to get too hot around May and June, you definitely want to avoid that if you can).
i've lived in Baton Rouge my whole life, and i got married in BR on March 8 of last year. earlier that week the weather forecasters had been calling for uncomfortably cold weather and likely rain on our wedding day. but we lucked up. the rain and cold front came late, the weather was beautiful, and the temperature was perfect. it's usually pretty warm by April, March is generally more comfortable.
also, locals can tell you about the infamous "pre-Easter cold snap" that happens every year in BR. things have usually warmed up to a pretty comfy temperature by Easter, but every year, like clockwork, there's a cold snap just before Easter. not sure where you're from or what "kind of cold" your used to, but Baton-Rouge-cold is a humid kind of cold, and it can be surprisingly brutal. it's purely anecdotal, nothing scientific about it, but...well, based on my experience, i wouldn't plan anything within a week or 2 before Easter.
and i also would like to make a recommendation. for formalwear, Luxury Limousine and Formal Wear on Airline is a great place. they are completely local. with the big tux rental chains, they ship their tuxes all over the place, and if, on the day before the wedding, someone picks up their tux only to discover that it fits very poorly, you'd be hard pressed to get a better-fitting tux in the exact same style from them on such short notice. with Luxury, their warehouse is here in Baton Rouge. period. there is no "oh, we have that tux in a 48 in Houston, but i don't think we could get it here on time". it's all here. the guy that runs the place is amazingly knowledgeable and helpful, plus their tuxes generally are in better condition and less worn than the ones you get from the big chains.