Peluche is a feminine noun, but the gender is a male. Am I only able to say petite peluche because the object only has a feminine form?
Correct: the grammatical gender counts more than the semantic gender.
As an alternative, you can state what the animal is. The formula is X en peluche. Compare
J'ai reçu une petite peluche comme cadeau ! C'est un ours.
J'ai reçu un petit ours en peluche comme cadeau !
But you're out of luck if you have a male stuffed mouse, because that'll be une souris en peluche !
On the subject of grammar not aligning with reality,1 another one that people frequently stumble over is personne. You're grammatically une personne whether you're man, woman, or other. You can avoid this by a similar means — or don't avoid it. French speakers aren't confused by a sentence like « Une seule personne est venue à ma fête, c'était Armand. »
This is the traditional answer, anyway. Some of the rules about grammatical gender have been challenged, but I don't think the challenges have mainstream acceptance. Other users living in French-speaking cultures might be able to say.
1 Not that a peluche has any gender in reality, regardless of whether you call it a boy or a girl :)
"Peluche" and "personne" are definitively a feminine noun. But one may speak of a man being "une personne". This is no problem in French. And this happens for many words in French. The word "sentinelle" is feminine, although usually this role is held by a man. A new member in any society is always called "une recrue" even if it is a man. You can believe me. I am speaking French !
In French, inanimates (objects and concepts) have arbitrary gender and the animates (humans and animals) have gender correlated with sex. Nouns referring to males are generally masculine and nouns referring to females are generally feminine with some exceptions. Usually there is a neutral noun for species or unisex consideration which is either masculine (chien) or feminine (vache), and sometimes there is only this neutral noun available (souris_F, rat_M, sentinelle_F, mannequin_M).
- une souris mâle
- un rat femelle
- Henri, la sentinelle impressionnante
- Sophie, le beau mannequin
The adjectives, the determiners (and some past participles) agree in gender with the noun. The only exception is the noun GENS (always plural) which triggers feminine agreement with the preceding adjective les petites_F gens while triggering masculine agreement in all other contexts les gens étaient contents_M, les gens petits_M.
NB. The noun phrase has masculine gender even with a feminine adjective les petites_F gens seront contents_M.