Just to add to what seth said...
Think of what the yeast you use is cultured for.
Fleishman's yeast is developed as a levening for bread. It is quick to activate and proof dough. Since the yeast is killed off in the oven, the yeast is never really intended for long term fermentation.
I am not saying that you can not have success using bread yeast. You can, but you are opening the door for big problems that your bread yeast was never intended to deal with.
Wine yeasts are rather inexpensive ($2-3 delivered), so if the price is what you are concerned with, you have nothing to worry about.
Also, like seth said, there are many different advantages with many different types of yeast. I know a number of folks choose to go to the EC-1118 strain (a yeast used for champagne) as their all purpose yeast. I tend to shy away from this strain unless I am going for a high AVP in my final product or if I am looking to go sparkling (the intended use for this particular yeast). For a standard red, I might go with R212 and I might go with D47 for a classic white.
You do not mention what type of wine you are making. Given more information, we could recomend a yeast more suited to what you are doing. I would recomend that you get a wine yeast suited to what you are making and do a bench trial. Use flieshman's in half and the wine yeast in the other half and then check out the difference in the final product. The results will surprise you!