Henry Beck's first drawing has been reproduced elsewhere ('Mr Beck's Underground Map' by Ken Garland, 1994, Capital Transport). It was submitted to the RATP (the Paris transport authority) in the late 1940s, and rejected for reasons not entirely clear. There is no evidence that the second attempt was submitted to the RATP.
Mapping the Paris Metro is a particularly difficult project for any graphic designer to undertake. The dense network of highly interconnected lines demands great skill in showing them with balance and clarity. Part of the difficulty arises because lines cross Paris at distinctly awkward angles. Deciding at which of the permitted angles to draw them (horizontal, vertical, or 45 degrees) needs some care, and inappropriate choices can result in all sorts of unwanted side effects.
For both attempts, Beck made Line 1 his major axis, but as a 45 degree diagonal slicing across the map (in reality it runs at around 25 degrees to horizontal). This results in awkward compression around Bastille and wide open space around Etoile. Even so, to the untrained eye of a British observer, this can look like a clever solution. On the other hand, to a Parisian, the entire City of Paris had practically been rolled onto its side. With the lack of clear colour coding for the Paris network, the Paris RATP officials must have found the map deeply disorientating and confusing, and the many errors on the map would have given them an easy basis for rejecting it.
Realising Beck's second attempt was reasonably straightforward. He had managed to merge Montparnasse-Bienvenue, but in the process two stations vanished; Vavin and Edgar Quinet. Adding these required some reconfiguration in this area. Annoyingly, Beck's many spelling mistakes tended to shorten station names, so that correcting them caused problems fitting them in. I dealt with this by using a condensed typeface. Beck's choice of colours did not match contemporary official maps, so these were altered to match. Finally, the Sceaux Line needed to be added in order to give the map a more authentic appearance.
One of the hardest parts of implementing the map was choosing the right typeface. Unlike London, the RATP had not by that point evolved a comprehensive corporate identity, and maps tended to be hand lettered in a style very evocative of Paris of the period. The problem is that implementing hand lettering is very difficult to do convincingly on a computer. Look at any Paris Metro map of the period, and you will see that no two letters are quite alike. They might agree in their general forms, but fine details such as line thicknesses and precise forms vary. This makes creating a satisfactory computerised typeface almost impossible. Selecting a condensed typeface contemporary with the map was also an unsatisfactory solution. Univers had not been developed at that time, Gill Sans would have been unthinkable, and none of the various 'Grotesk' fonts (early sans serif) quite matched the letterforms used on the hand-lettered maps, capital R, G, and Q being particularly difficult to match well, with C and S also causing trouble. The solution, a modern typeface surprisingly close to the hand lettering, was discovered by accident after extensive searching. We have to imagine that the RATP decided to develop a typeface closely based on the hand lettering of their designers, an event possibly no more far-fetched than their adopting Beck's design for their network.