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Night transportation

The majority of public transportation in Paris stops at night. Many of the buses stop around 8 PM and restart again at 6 AM, and others stop around midnight. As for the métro, the hours vary, but in general the last métro departs from the beginning of the line around 0.30 AM (1.30 AM Friday and Saturday). The first train leaves around 5.30 AM.
The hours of the first and the last train are posted in each station. 


Public Night Transports by bus - Noctilien.
The public transportation in Paris stops during the night. Many of the buses stop around 8 PM and restart again at 6 AM, and others stop around midnight. As for the metro, the hours vary, but in general the last métro departs from the beginning of the line around Midnight. The first train leaves around 5.30 AM.
To facilitate travel at night, Paris has introduced a new night bus service called "Noctilien". It operates in the greater Paris area every night from 12:30 AM to 5:30 AM.


Taxi
The taxi could be any car model. They're usually large sedans. Important warning, if the taxi doesn't have a meter inside, don't take it... 
When you call a taxi company to come pick you up, the driver starts his meter running from the moment he leaves from where he is when you call. If the taxi is far from you when you call, it's possible to already have 7 euros on the meter when he arrives. In general, they usually send the closest taxi but, there may not always a taxi close by.
Tips for the driver, usually around 10% of the fare but not mandatory.

Here are some rules you should know when it comes to taxis : 
- You don't have the right to hail a taxi less than 50 meters from a taxi stand. The taxis that are waiting there have priority over taxis that are passing by. 
- At a taxi stand, you have the right to choose the taxi that you want (nothing obliges you to take the first one in the line). 
- A taxi can refuse to take on passengers if he is at the end of his service (each taxi only has the right to work a certain number of hours a day, and the end of their service is posted on a meter in the back of the car). 
Taxi G7 - +33 1 47 39 47 39 
Taxi Bleu - 0825 16 10 10

Obivously Uber is available all around Paris, other options are

FreeNow
LeCab