What is the main idea of the Morozevich variation in the French vs. the Tarrasch? What is the main idea of the Morozevich variation in the French vs. the Tarrasch variation? 


  1.e4 e6 2.d4 d5 3.Nd2 Be7


In other words, how can Black benefit from the slightly unusual development of the Bishop before the Knight?
3...Be7 is mainly an attempt to side-step some of the other well-known theoretical variations, while making white to first commit another developing move before deciding how to continue. For instance, the usual 3...Nf6 often leads to 4.e5 Nfd7 and black has already committed the knight to d7 while white has all three attractive options of Bd3, f4 (further discussed in the 2nd diagram) and Ngf3. Instead with 3...Be7 first, many more alternatives survive, such as:

All diagrams contain annotations.

 [title "3...Be7 possible follow-ups in Tarrasch variation"]
 [fen "rnbqk1nr/ppp1bppp/4p3/3p4/3PP3/8/PPPN1PPP/R1BQKBNR w KQkq - 2 4"]

 4.Ngf3 Nf6 5.e5 Nfd7 {You see by simply having delayed Nf6 by one move and kept an option such as Nh6 open, white's choice of 4.e5 5.f4 is already less attractive} (4.e5 Nh6 {taking advantage of the early Nd2 blinding the h6 square for white so the knight can now re-route via h6-f5. This maneuver is also often employed in f4 variations of the French.} 5.Bd3 c5) (4.Bd3 c5 5.c3 cxd4 6.cxd4 dxe4 7.Nxe4 Nf6) (4.Ngf3 Nf6 5.e5 Ne4)


So in the above side-lines not only has black kept some additional options open with 3...Be7 but it has also made a couple of key variations less attractive for white, such the usual f4 lines in the Tarrasch (which is also briefly touched upon on the wikipedia page of French Defense), for example:

 [title "classical 3...Nf6 and the f4 variation - compared to 3...Be7 :"]
 [fen "rnbqkbnr/ppp2ppp/4p3/3p4/3PP3/8/PPPN1PPP/R1BQKBNR b KQkq - 1 3"]

 3...Nf6 (3...Be7 4.e5 c5 5.c3 Nc6 {You see the difference now more clearly: 4.e5 is no longer with tempo, thus allowing black to start undermining the central pawn chain with c5 one move earlier, followed by Nc6, practically never allowing white an easy route towards the previously mentioned main variation.}) 4.e5 Nfd7 5.f4 {notice the knight's already on d7} c5 6.c3 {nothing really challenged white's f4 play}