Hi Anori,
Thanks for your reply. I`m going to have to print it out and study it. Scrolling back to your method I can see a couple of points which may be causing you problems. Point 3: add the water to the reduction before you add the egg yolks - as the temperature at point 2 may be too high for the egg yolks, I would suggest that you add the water before you add the egg yolks.
I`m scrolling back, reading and thinking as I write this and one thing that I notice is that you say you`ve had the sauce in France. Now this means that you have a "bench mark" in relation to the taste of final product that you want to achieve. Next question - how many times have you tasted the sauce - I reckon it will taste differently in every restaurant depending upon which butter is used and which acid ingredient is used, the quantity of herbs used etc! However, there are some "certains" that you can quarantee. It should taste buttery, herby, eggy and acidic at the same time - it is the most mellifluous of sauces and consequently most difficult. Sorry, I`m not making things any easier here am I? There are 4 flavour notes, rather like the scales of music - which one was the predominant one for you? against which you can measure your sauce. Which flavour PEAKED for you? Which flavour do you want to be the highlight - in order to answer this question you need to cast you mind back to what you tasted in France. From your postings I would suggest it is not that of butter (which is best clarified before you add it). I would surmise that you want the flavour of the shallot and herb reduction to come through a bit more, counterbalanced by the acid - vinegar in the reduction or lemon juice at the end of creating the sauce.
Finally, it may be that the amount of finely chopped tarragon you are adding to the sauce, after incorporating the butter, is insufficient to give the depth of flavour you want. Add a bit more and add a teaspoonful of freshly chopped flat leaved parsley to the sauce to warm through whilst it is in the bain marie or keeping hot before you serve it.
Whilst I`m studying your recipe I reckon you should give it another go bearing in mind the points that I`ve made. I think the critical thing here is to think back and indulge in some "mind tasting" recollections. Again, every thing comes back to what was the END point of the sauce that you tasted in France which is the FIRST and LAST point of tasting for a customer - buttery, herby, acidic, eggy or some other combination?
Hope this helps - let me know if you need more info!
All the best,
Archiduc