"France" pronunciation; /æ/ vs. /e/ in American accents
I agree that your second pronunciation from Oxford Learner's dictionary was hard to distinguish. It sounded like it may have been a more southern US dialect. See the Pin-Pen merger.
Wikipedia has a pretty good explanation and table showing variations in accents of American English due to /æ/ tensing. Depending on the consonant following /æ/, the sound may be raised, lengthened or diphthongized. In my central Canadian prairie accent, it's hard to distinguish a difference between parish and perish.
There are simpler word pairs to distinguish these sounds. Try bat and bet.