I'll travel to Paris, France in June. For my musical studies, I need to practice violin 5 hours every day (~ 84-103 dB), alone. Is there any place I could use in Paris for such purpose, if possible at a reasonable price?
Rent a (Solo) Music Studio
Since you mention the need to be alone, a dedicated music studio comes to mind. A quick google search revealed Studio Luna Rossa in the 13th Arrondissement and Maison de la Musique in Neuilly-Sur-Seine 92200. Both of these offer small solo studios for something around 6-7
EUR per hour, during both weekdays (off-peak and peak hours) and weekends. Whether this is considered as cheap is up to you to. :) There must be more music studios available for rental out there. These are just two examples. To find more you might want to try querying your favourite search engine for salle de musique and/or studio de répétition (French for music studio).
Parks and Kiosques
If you decide one day that you want to see something else other than soundproofing foam in Paris, you could head to any park, set up your gear on the grass and go nuts. Indeed it is not uncommon to see random art performers rehearsing in the Parisian parks. Here is a map of all the parks in Paris and Ile-de-France metropolitan area.
Moreover some parks have dedicated music gazebos (kiosques in French) with great acoustics. These are usually free to use. Note that from May to October some kiosques will be taken by the annual Kiosques en Musique musical event, whose full 2015 program can be found here. If you wish to use the kiosques you'll want to coordinate yourself with these events. Here is a map of all the kiosques in the Parisian parks. Below is a picture of the kiosque at the Parc du square Necker:
Le kiosque à musique du square Necker, Micheline, Fair use
Park Regulations and Musical Instruments
Note that is is technically forbidden to make noise and disturb other park users, as per the parks rules and regulations established by the Mairie de Paris. Moreover these explicitly mention noise arising from playing instruments:
Sont interdits les bruits gênants par leur intensité, leur durée, leur fréquence ou leur caractère agressif, en particuliers ceux produits par les instruments de musique et de percussion et par la diffusion de musique amplifiée, sauf dérogation.
Whilst this does indeed mean that you need to ask the Mairie de Paris for authorisation to play an instrument in the park, in my humble opinion you should be able to play freely so long as you don't disturb others around you. Whether violin music is a nuisance due to its intensity, duration, frequency or aggressive character (translating the afore-mentioned rules) is up for discussion. In any case, keep in mind that you are doing something forbidden and that therefore people might ask you to move or stop.
The metro stations were a good option when I was in Paris 40 years ago.