It seems I'm more optimistic than the previous responders on this one. Yes, I've found it takes a little convincing to get clients into the idea of film photography but that's where a good portfolio steps in to help out - make sure you do a lot of your own work developing your skills and a collection of relevant material for whatever jobs you pursue. It's usually the case, particularly if you are doing event work (weddings, etc.) where the deadlines are not as short as they might be for commercial photography or journalism, that clients wont care what you shoot with - some may even like the idea of film work (you can sell on the benefit of longevity, tangibility, etc.) You should be aware, however, that you will most likely have to present digital products at the end of the day so you have to get used to the idea of scanning your negatives or prints so investment in a decent negative scanner is a good thing to start with if you know that you will be pursuing this for a long time; many places that process film can also scan it but it will be more costly and you will have less control over the end result.

A note about formats: please do some reading about 35mm, medium format (i.e. 120 film), large format and decide what you think would be easy for you to work with and what will present the best results. I shoot my professional work with medium format equipment - there are lots of options here so you should look around - basically with a 6x7cm negative (for example) you have a lot more to work with than a 35mm negative and therefore the fidelity of your image, if blown up for magazine work or some such thing, can be a good deal higher. Anyhow, there's lots to figure out about equipment and the like and I don't know what field you're interested in working in so I can't recommend anything further for now.

If you love the work then you probably wont mind spending more time on your projects (processing, printing/scanning, etc.) and I can assure you that with a developed portfolio and a confident attitude you will be able to sell the idea of film to more people than you might imagine.