ASL is not quite the same as LSF but syntactically - it makes sense. ASL is a visual language. ASL following a verbal language makes absolutely no sense for people who can't hear. don't think of ASL as a french language just because it follows french grammar. it's not really quite the same. from the very beginning, it has morphed into American Sign Language.
if you have trouble using ASL in ASL format... that's ok. it's fine if PSE/SEE works the best for you. I sign in PSE/ASL and I'm still learning how to sign in ASL fully.
trust me - you will like ASL better than foreign sign languages (except LSQ/LSF/LSFS). foreign sign languages such as chinese, japanese, etc. are dependent on speech while ASL isn't. many foreign sign languages have same signs for many things. that's just terrible. that's why it's dependent on speech.