Luckily, for washing machine it's the same (female) but with others like sun, moon, or table we're not so lucky. And German having three genders for words and french only two often makes things more complicated.
There are some, but many nouns you just have to remember. Diminuitives are neutral, living beings commonly use their biological gender. There are many exeptions, but knowing the origin of them helps (e.g. girl -> das Mädchen is a dimiuitive of maid -> die Maid)
It helps reading books or watching shows/movies in german to get a feel for the gender of nouns.
Hopefully somebody can give you a better answer, but being a native speaker, I’ve never really thought about it. I can’t say anything comes to me as obviously explaining the genders of different words.
Also German is quite systematic in its naming of things (surprise surprise), so specific names have the same gender as the more 'generic' root word for the thing