You are right that 'would' can sound more formal than 'will' in requests. 'Would' is the more tentative and hypothetical version of 'will'. That is why 'Would you help me?' sounds more polite than 'Will you help me?'.
'Will' is often used for future time:
J'aimerai = I will like/I'll like
J'irai = I will go/I'll go
Je le ferai = I will do it /I'll do it
'Would' is used for hypothetical situations:
J'aimerais = I would like/I'd like
J'irais = I would go/I'd go
Je le ferais = I would do it/ I'd do it
We use 'will' for probable situations in the future, for example:
Si tu étudies, tu réussiras à l'examen = If you study, you will pass the exam.
We use 'would' to imagine unreal and hypothetical situations :
Si tu étudiais, tu réussirais à l'examen = If you studied, you would pass the exam.