EDIT : thanks to a very good remark, I must edit this answer and apologize : I was under the false impression that french was the international language of medieval emblazonment, but it seems not to have been ; France was historically a land of chivalry in which heraldry was important, but I was wrong in saying it was exclusively said in french, as I was just able to find sources of late medieval german emblazonment.

First of all, this coat of arms blasonne as "de sinople à trois fasces d'argent. Cimier : un buste de femme au naturel, vêtue, chevelée et couronnée d'or, les bras remplacés par des proboscides aux armes ; lambrequins de sinople et d'argent.".

Here is another representation of the same crest.

If you're not familiar with the concept of "blasonner", which translates as "emblazon", it's the science of coat of arms and their description. It was historically exclusively done in french (nowadays, you can emblazon in any language, although many terms are directly imported from french) it was born in medieval Europe out of the need for identifying knights and nobles and, if done correctly, will always produce the same coat of arms you "described".
EDIT 2 : a small addendum on the history of heraldry : the first known written sources of heraldry as a discipline dates back to the 11th century, and the discipline wasn't only about knowing to describe a coat of arms, but also to be able to quote the titles and accomplishments of the noble !

Back to our coat of arms. It is divided in two distinct parts that you can even discern in the blasonnement : the shield, which bears the colors of one's house, and the crest, which isn't always there and bears decoration. This decoration often represents the role, responsibilities and dignities of the owner of the coat of arms. It means that, whilst the colors on the shield are always the same among a house, the decoration can vary based on one particular person's responsibilities.

In this case, I found that this particular version was adopted as the Fleckenstein "standard" coat of arms, so it didn't represent everyone who used it, but this nonetheless tells us that the first person to use it was probably a soldier or a knight (maybe Wolfram, who was a high-ranking soldier). Sadly, the helm cannot help us further, as there is no standard between the helm's appearance and a specific role.

Finally, to answer your question about the lady, her arms are emblazoned as proboscides, which means trunks (as in elephant trunks). It is a rare ornament that mostly exists in german coat of arms. As for their signification, it is hard to find one, but a suggestion is that they represent horns ; horns are both used to symbolize dignity and power.From there, two possible explanations :- either the lady herself has a signification that was lost in time, and she is the person of dignity and power, but it's unlikely ;- or the bearer of the coat of arms is the person of dignity of power, and it is linked to the helm, which leads us back to the interpretation of a high-ranking officer.

I'm going with the latter, as the function of Maréchal de Haguenau was tied to the Fleckenstein family name, which would very much explain the use of this version until the extinction of the Fleckenstein agnatic line during the 18th century.