It's simply practice. You'll get to understand any accent simply by listening to it and recognising the patterns. Some sounds in English are either different or nonexistent in French, so a French person would substitute these sounds with their own French habits. You might have heard the R at the back of the throat, a dropped H, and TH changed to either a T or Z sound. Maybe some words which are similar in French and English received the French pronunciation. Please don't ever worry too much about it, just look for examples online - it's really quite enjoyable to listen to accents. :)

Learn French.