It would be "la fille mange" and "les filles mangent" la and les sound different, so you can tell whether it's femme or femmes respectively.
All you have to do is memorise the differences between la, le and les. Listen to the audio over and over, AND/or go to google translate and press the loud speaker button.
my advice to you is....dont look at English meaning of french words ...it is for your understanding....do not co relate french words with English meaning..... in English eat remain eat (or eats) no matter She, He, They, you, we..... I am from India...my mother tongue is "Marathi" Indian language...in which Eat mean KHA... I do not expect you look into deep meaning but KHA (EAT) word changing in our language too.....I/Me Khato, He/To Khatoy...She/Ti Kahtey...they/Te Khatat... We/Amhi Khatoy... all mean EAT in English but words spelling changes not meaning... I can see if any one use wrong words KHA the it will be funny and some time disrespectful... so similar things will happen by using wrong mange/eat.
So understand there are many people in world who speaks different languages without knowing English or without knowing their words English meaning..... still they speak their own language fluently :)
so do not co-relate with English... Learn french as a independent language :)
more likely to eat 'du' boeuf than le boeuf although in special context it may be possible. Remembering Boeuf is primarily the ox meat. So in the wild perhaps the lion eat the ox? And here it's a little quirky as with the plural of boeuf it means again the animals not the meat. "les boeufs (silent f) tirent la charrette) the oxes pull the cart. )