I want to submit a "demande de stage" in person.
Please, in French culture, should it be hand-written or typed?
À moins que la candidature se fasse par courriel, la lettre de motivation doit être manuscrite, le Curriculum Vitae est typographié.
Unless it is by e-mail Curriculum Vitae has to be typed, for easy reading, but motivation letter is hand-written to expose clearly your personnality (pay attention to it, it is often a important piece when candidates have similar C.V.).
If your writing script is not easy to read, you can type your motivation letter and hand-write the last paragraph.
Unless you are clearly asked otherwise, you should type both your curriculum vitae and motivation letter.