[en] ? ligne 10

I would like to know if there are some trains are going regulary from Porte d'Auteuil to
Michel-Ange Molitor.

Half of the trains on line were doing this during the past. Nowadays only a few exceptions still do it, including the very first train of the morning.

At first line 8 served the loop passing by Michel-Ange Molitor in 1913. But by 1937 line 8 had been extended to Balard so line 10 took over the branch to Porte d'Auteuil via the loop. In 1980, it was extended to Boulogne - Jean Jaurès and as @metroN said, one train out of two was running through the loop. It is yet unknown when this service stopped. This being said, he is right about the fact that the first train in the morning goes through the loop. Although I highly doubt anyone is enough of a rail enthusiast to wake up at 4:30 AM to take this train...

By the way, if you want to see the evolution of this place, I know of a video with English subtitles...

I already saw at the end of a morning in June 2018 a train terminating at Porte d'Auteuil on the central track in order to run through the loop towards Michel-Ange - Molitor. The passengers had to take the previous train which waited for them on the usual track (on the other side of the same platform) before leaving towards Boulogne - Pont de Saint-Cloud. I saw the other train entering Michel-Ange - Molitor a few minutes later.

Thank you for the answers. I know about the history of the network
I am planning in january a "ralley du metro", but i want to use only the parts which exist 1953.
(-> https://lignes-transports.forumactif.org/t356-rallye-du-metro )
So i would like to take the loop if there is regulary service (without waiting long) - otherwise
i will walk frome Porte d'Auteuil to Michel Ange Molitor.
Starting at 4:30 am is a little bit too early

So... this means you wouldn't have to deal with any branch, in fact...

Since @metroN says he once saw a service running through the loop in the end of the morning, then this could mean that some services in rush hours go through the loop.
Also, if you need to know if it goes to Porte d'Auteuil - only take trains that stop at the central track in Porte d'Auteuil ! Only these will call at Michel-Ange Molitor.

By "end of the morning" I meant around midday approximately, so not sure it could be considered as rush hours.

Je ne parle pas l'Anglais , si l'on pouvait s'exprimer en Français ?

C'était pour éclairer l'auteur quant à l'utilisation de la boucle de la ligne : il se demandait s'il existait encore des trains qui parcouraient le bout de boucle entre Porte d'Auteuil et Michel-Ange - Molitor délaissé par les circulations habituelles ayant Boulogne - Pont de Saint-Cloud pour terminus. On a donc répondu que de rares trains, dont le tout premier du matin, le faisaient toujours au lieu d'aller à Boulogne (comme dans les années antérieures à 1980 où ce prolongement en banlieue n'existait pas encore et que les rames repartaient directement vers Gare d'Austerlitz), alors qu'au début ça concernait une rame sur deux. J'ai rajouté qu'une fin de matinée en juin 2018 j'avais déjà vu un train faire son terminus sur la voie centrale de Porte d'Auteuil pour ensuite repartir vers Michel-Ange - Molitor ; les voyageurs devaient se reporter sur le train précédent qui les attendait sur la voie principale de circulation (celle au nord), ayant donc stationné quelques instants avant de poursuivre vers Boulogne.

Oui, j'étais persuadé que "fin de matinée" ce serait 10h.