I quite understand that you were playing within the scope of the rules. Your explanations were very clear in the detailed description of the game. It was great to have the photographs too, thanks.
Here is how the same situation might have 'played out' in reality. The German force would have come onto the table with a point guard. The rest of the force would have followed on in line of march. The point guard might have been an officer, cyclist, or infantry scouts patrol. Its role would have been to detect the French defenders, who would not have been visible (despite les pantalons garance). Detection of the defenders would have depended on when they chose to fire against the point guard, or when the patrol ran right into the defenders who had elected not to fire. The latter option would have been very unlikely.
As soon as the defenders opened fire on the point guard then the patrol would have gone to ground in an effort to spot where the fire was coming from. Because the point guard would likely have been split into two with one part bounding while the other stayed down to observe, the stationary part of the patrol would have detached a runner/s to alert the march column. Remember that at this point, in reality, the Germans would not know the full size of the defending force. The patrol would have had a sense of the volume of fire that they received. Being unable to see the defenders (unlike the players), however, the patrol would not know if only some of a larger force opened fire. The only thing the patrol would know for sure is that the fire came from a general direction.
Once the march column was alerted, it would have shaken out from the lines into more open formations. An infantry battalion would have dispatched a company forward in the first instance. The company would have arrived in waves. The company commander or adjutant might well have gone forward to link up with that part of the patrol that had remained stationary and on watch or providing covering fire for the forward elements of the patrol in order that they could withdraw. Having confirmed the general direction of the fire and some sense of its volume from the reports of the scouts, and assuming that the lead elements of the infantry company had not come under fire already, then the company commander would have set up a base of fire. A platoon size element might have taken up a firing line and opened suppressing fire in the direction of the defenders presumed location. A second platoon would have manoeuvred forward to the right; a third platoon to the left. These platoons would have starting bounding forward, probably by section in the first instance. If either manoeuvre element had come under fire as well then it would have ceased bounding and formed an additional firing line, extending the base of fire of the first platoon. At this point, assuming that all platoons had taken fire, then the company commander would have known that he was up against a more substantial force of defenders.
If the defenders fire had become more heavy then the company commander would have sent back word to the battalion commander, who would have coordinated one or more additional companies to move forward in support. At this stage, any additional fire support systems such as machine guns and direct fire artillery assets might have been directed forward too. Generally speaking there wasn't a rush to move these forward though in the first instance.
Back to the company that was engaged in the firefight. The company commander would not have waited for follow-up support unless the defender's fire was very heavy. The commander would try to determine if there was a potential weakness in the defender's position, whilst seeking to understand where the defenders might also be lurking. In the case of the defenders in the (beautiful looking) house on the French left, the German commander most likely would have sought to bring the last platoon into play by manoeuvring around to the flank of the house, on the side furthest from the bridge. The aim would have been to bring the French defenders under enfilade fire.
At some point the outnumbered French defenders would have likely been suppressed by the increasingly heavy rifle fire. Some of the defenders might have broken to the rear but the other sure sign would have been that the volume of fire fell away. The German force would have continued to manoeuvre by bounds of sections or smaller, bring the base of fire closer to the defenders. In most cases that I have read, the defenders usually collapsed and surrendered or fled. It was rare for an assault to come to the point of the bayonet. Very few wounds were inflicted by bayonet.
At some point, depending on the orders of the French defenders, the other French element would have joined in the fire fight. This would have immediately increased the levels of uncertainty in the German command. It would have reinforced the need to keep up pressure on the first set of defenders from the flank that was furthest from the other defenders. The process of deploying a new base of fire would have been repeated, aimed at the new source of fire. This scenario would very likely have triggered the deployment forward of the machine gun section (very unlikely to have been more than one section involved) and any artillery assets that were available. Their movement forward could be justified because the size of the defending force now seemed to warrant it and because sufficient fire power was being deployed with riflemen to protect the MGs and guns coming into action. The pre-existing protective fire was especially important where the approaches to the enemy were so open, as in the case of this beautifully set up battlefield.
I hope these observations are of interest.
You have already noted that the mortars could have been considered as artillery. They were performing the same role, attempting to suppress the defenders. It could equally be argued that the point patrol had done its work by the time that the game started. The game mechanics appear to allow for manoeuvre without fire, i.e. it is better to push all infantry elements forward without having any of them lay down additional suppressive fire. Faced with a similar situation in real life, a German battalion commander would have done the same ;-). In reality however, the effect of defensive rifle fire was so devastating that the process of building up a fire base whilst ascertaining the size of the defending force, lines of approach, etc was paramount in the minds of attacking commanders.
Robert