Learn as much French as you can. The ability to actually speak the Romance language will improve your pronunciation and increase your understanding of the cadences of French speech. Knowledge of working French can also provide your accent with authenticity and verisimilitude.
Speak English with a musical lilt. The French language often uses a pitch that goes up and down throughout a sentence. Questions are frequently spoken with an upward pitch as the end of the interrogative phrase is reached.
Include silent "H's" into your speech. Words like "helicopter," "hotel," and "however" sound much more French when pronounced without the consonant in front.
Adjust your "e," "r" and "th" sounds as well. "E" vowels are elongated in the language. The back of the tongue in the back of the mouth produces the softer, more guttural French "r." Replace hard "th" sounds with "dz;" for instance, "this" would sound like "dzees."
Take a possible French dialect into consideration. French is spoken differently in different regions. Differences exist between Parisian and Marseillais speakers, for example. There are also such variants as African French and Canadian French to consider. Look into the background of the character you're portraying to determine the exact type of French to replicate as an English speaker.
Look for dialect books and audio CDs to help you practice and refine your English as spoken by way of French. Consider hiring a speech coach to support your aims as well. An expert in dialects can provide you with immediate feedback on the success of your accent and help you to use it with confidence.