The literal translation, like for the iPhone game, is "oiseau chanceux", which does not mean anything really in French.
The translation of the expression "lucky bird" meaning a bird (and by extension, a person) with its belly full, does not exist.
There are however several adjectives or expressions to describe this physiological state, but I don't know if this is what you want. Here are some: repu, rassasié, avoir le ventre plein, or from a famous song, avoir la peau du ventre bien tendue.
It is the beautiful bird which gets caged.
It isn't lucky to have bird poop on you.
A complete sentence would read: Voir ce bel oiseau? Bel oiseau is the direct translation of beautiful bird.
Bird in French is l'ouisseau. (phonetically: la'wazo)
The direct translation of "bird" from English to Greek is "πουλί". There are also many variations of this translation depending on the specific type of bird.
the Chinese translation for cherry blussom bird is:ying hua niao
a bird is 'un oiseau' (masc.) in French.
In French bird is male
Turkey
Manu
iphone
Most likely it just means a bird just landed on you.