French advance variation
You could use an engine I suppose, but you are playing weird moves to just get a regular Advance French a tempo down.
Opening Name
French Defense: Advance Variation Paulsen Attack
Pgn Notation
1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Nc6 5.Nf3
I don't know why you want to spend time studying a bad opening. To each their own, I guess.
I agree Sveshnikov refuted the advance years ago.
Matthias Wahls also explained this as arising also from the O'kelly Sicilian...funny no one recognizes this position much.
The OP asked for recommended resources to study. In these days of on-line tools and massive databses books are still useful. This is my favourite:
The French: Tarrasch Variation. Steffen Pedersen. Gambit 2005
Also all the editions of Watson's "Play the French" have intersting material, but they are less comprehensive.
NOTE: I made the mistake of selling my earlier edition when the latest one came out, thinking the new edition would be an update. In fact each edition is a major re-write of the previous one, with very different recommendations in some systems. In particular he has dropped a lot of great analysis on the Advance variation and his new main recommendation is a peculilar, unnatural and (to me) dodgy looking line.
Althought these recommendations are not up to date they should be more than enough at less than master level.
Ther are many GMs and IMs, past and present, that have the French as their main defence to 1. e4. Uhlmann's games include many good examples of breating up the White in the Fremch "counter attack". Most of the precise variations he played have been improved for one side or the other since his time, but I don't think there ar better games for showing the principles of the French. That is, how to use the advantages that the French gives Black while avoiding being smashed on the King's side, or squashed into passivity. Korchnoy is a good example for seeing the defensive resources in awful looking positions. Nigel Short's games show more variety and experimentation in the French.
Hope this helps.
You can play any garbage in blitz games. Playing c6 then c5 likely wins a few seconds. There is no positional/ chess benefit in playing this way.
Play e6 sicilian's and french myself, there are positions that can transpose. The particular line you are interested in is just tempo down on known lines for no benefict, at best. The point of a6, is to follow up with bd7-b5 to exchange the bad bishop. If play normal advance french moves ne7-f5 or g6, then it, a6, does't have any point either. Think your mentor is confusing you with a terrible combination of bad and complicated ideas.
In most variations of the French (and most other semi-open games) Black will eventually play a6. If played when needed, it can be a big help. If played out of sequence in an opening, it could be a disastrous waste of a move. Here on move 6, it looks like a pointless time waster.
The position may be arrived at by 1 e4 e6 2d4 c6 3 Nf3 d5 4 e5 c5 5c3 a6 6Bd3 7 cxd4 Nc6 8 Nc3 Nge7 After white castles...black can play Ng6 or Nf5. One site call masterchessopen.com calls it the French advanced Paulsen Najdorf which means it bears resemblance to the Sicilian Najdorf. The move c6 to c5 is played due to the fact that black can also transpose to the stonewall defense depending on what white plays.