If you like the Caro, let's imagine : 1.d4 d5 2.e4 c6, ok it his actually the starting position of the Caro but after Nc3, main move, black plays 3..dxe4 and now 4.f3 enter in the BDG Ziegler defense if he take the pawn, or enter in a type of game that the BDG player want even if you doesnt take on f3. Against the french, White can't force Black to reach a BDG, but there is some pseudo-BDG like the Alapin, the Diemer-Duhm, or if Black plays system like the Rubinstein : 1.d4 d5 2.e4 e6 3.Nc3 dxe4, the BDG player can try to enter in the Euwe defense of the BDG with 4.f3. And if he plays the classical French with 3..Nf6, then standard french move 4.Bg5, and again, if he take on e4 I play f3, and can transpose in the Euwe, and if he plays the MacCutchon or Be7, then I play normal french with White, that a BDG player should know also.

I like 1.d4 d5 2.e4 e6 as well. 

I agree with MNb that the Blackmar-Deimar is not quite sound, but I like to win games rather than test my memory.  The French allows me to do this.   

Occasionally I face 1.e4 c6 2.d4 d5 3.Nc3 de4 4.f3.  In those cases, I try for ...e5 at the earliest feasible moment.  I have had great success with the French and this line of the Caro-Kann, but (fortunately) I haven't faced the BDG against strong experts or masters in serious play.  Maybe there's a reason for it?

Gunderam (5...Bf5) looks very good now!  I think 4...c6 and 5...c6 are also good and relevant to transpositions from the Caro-Kann.  However, looking at the game Schoupal-Bonsai has steered me even more towards the opinion that 5...Bf5 is probably be the most effective way to meet the BDG.  Also 4...Bf5 (recommended by Wahls) doesn't look bad either.  But here I am beginning to think that 5...Bf5 is the most effective and least complicated solution!  You have two good choices:  Bonsai's approach and Markovich's recommendation.  I am little surprised that I am only one who has voted for this move.   

A funny observation:  When the BDG supporters start claiming a draw for White, I think that is often a good sign that White is having serious problems.  It kind of reminds the scene in Monty Python and the Holy Grail where King Arthur is fighting the Green Knight (or was he black?!), and after this absurd fight sequence, the Green Knight says, "We'll call it a draw."  And as King Arthur walks away, the knight is taunting him, "Chicken!  Chicken!  I'll bite you with my teeth!" (or something very similar).  I am joking, but this sometimes reminds me of die-hards who get a little carried away.  Sometimes I wonder in some cases if the same person was given the same position without knowing it was the BDG, if they would be so supportive of the white side.

Well, I would not chicken out of accepting the Blackmar-Diemer Gambit.  If I were Black, I would play the Teichmann Defense Accepted, 5...Bg4  6 h3 Bxf3  7 Qxf3 c6.

What is your favorite way of meeting the BDG ?