I would recommend first seeing if you can reduce some of the noise. Audition 3 has a built-in Noise Reduction plugin (Effects -> Restoration -> Noise Reduction). If you aren't familiar with that plugin, here's a quick rundown on using it:
First, Select the longest portion of the audio that contains only the noise. Right-click the selection and click "Capture Noise Reduction Profile" which is by default "Alt+N" in Windows.
Open the Noise Reduction plugin (be sure to leave the noise portion selected). Again it's located under Effects -> Restoration -> Noise Reduction. Within the plugin you'll see quite a few variables that can be modified as needed. If you click the "Help" button there is some useful information there.
You can preview your current settings by clicking the "Preview" button. I listen to the preview with the reduction active as well as in "Bypass" so I can hear the difference. Once you're happy with the settings click "Select Entire File" and you can preview your settings to see what it does to the vocals themselves. If it starts to make the vocals tinny or start to sound like there's a flange effect, then you'll have to dial back the reduction.
I hope that helps, if you would like more specific recommendations for settings etc, you can send me the file and I would be happy to give my recommendations.