Expanded from an earlier answer of mine

One of the popular complaints about French military policy, both in the immediate aftermath of 1940 and continuing in the postwar, was that Belgium's adherence to neutrality hampered the overall defense of the West against Germany. Alistair Horne in his famous To Lose a Battle described Belgian policy as akin to the nursery the rhyme Three Little Pigs in which Belgian intransigence ensured that "in one stroke [France's] Maginot Line strategy lay in fragments." Horne and other commentators would assert that the Maginot Line should have been extended in light of Belgium's insistence that it was a neutral, and as such could not have belligerents stationed on its territory. Such critiques though miss key elements both of Franco-Belgian grand strategy and ignore some of the problems inherent in extending the Maginot Line into this region.

While Belgium's public face was that of a neutral, its defense policy was definitely pro-French and geared towards cooperation with Paris. There were significant war plans and cooperation between the two countries' military establishment and both conceptualized many of the same problems. The critique that the Maginot Line should have extended through the frontier border misses the key fact that French strategic thought saw the Belgian frontier with Germany as the proxy extension of the Maginot. One 1932 French General Staff document noted that:

Belgium, by its geographic situation, constitutes the glacis of our northern region. Besides, it considers France as its natural ally. In case of German aggression, it will very probably request our support and its forces would cover, at the same time as Belgian territory, the meeting of the French armies destined to fight at their side.

This conceptualization of Belgium as a glacis meant that the French general staff encouraged the Belgians to fortify the Albert Canal and Dyle River regions. While these fortifications were not on the scale of the Maginot defenses, they were not supposed to reach this level. Instead, they were intended to delay a German advance long enough for a link up of French and Belgian troops that would destroy the invading Germans in a methodical battle, hopefully along the flat plains around Gembloux.

This strategic plan made French fortifications along the Belgian border somewhat superfluous. The whole idea of French planning itself was predicated on pushing Germany to invade Belgium and then being delayed by geography and fortifications long enough for French forces to defeat them in a set-piece battle. The Maginot Line itself discouraged an alternate, direct thrust into France, leaving Belgium the only real option for German planners. There was some thought given by French and Belgian planners in the 1930s to fortifying Arlon region of the Ardennnes as a contingency plan, but not much came of it. Belgium was unwilling to cover the costs of fortifying this region, and even when the French offered to pay for it in 1934, the Belgian Foreign Minister rejected it. The official rationale was that this would have been too flagrant of a violation of Belgian neutrality, especially for a peripheral area.

Although Belgium's rejection of the French offer seems foolish in hindsight, there were solid reasons for it at the time. Defense appropriations were already quite high and the Belgian government was having trouble paying for the fortifications on the German frontier. The Ardennes region itself was rather poorly suited for fortifications, being quite hilly and wet. This was one of the reasons too why the French did not seriously consider extending their own Maginot fortifications into this region. Costs of the line were already quite high and the overall sentiment in the French high command and government was such man-made fortifications would be superfluous in light of the region's unsuitability for mobile warfare. Phillipe Petain was on record saying that the Ardennes was impenetrable and Gamelin described the Meuse River as "Europe's best tank obstacle." This however does not mean that the French military completely ruled out any attack through the Ardennes. The French high command estimated that because of the roads and geography, a German attack would likely take nine days to clear the forest and two weeks to reach the Meuse. If a German attack were to materialize in this sector, then the French high command believed they would have ample time to organize an efficient counterattack. In this scenario, the forest and the Ardennes's terrain were expected to act as fortifications that would delay a German advance like the Dyle fortifications.

The German thrust in the region would prove this expectation to be woefully optimistic. Fall Gelb's panzer and mechanized forces proceeded far quicker than most of the French high command expected, sixty hours to clear the Ardennes and a day to reach the Meuse. There were many voices within the French military that challenged this complacent attitude to the Ardennes in the 1930s. One of the local commanders, Colonel Bourguignon, conducted an exercise that demonstrated tanks could operate far easier within the Ardennes than French conventional wisdom dictated. In 1938, the commander of the French Second Army, General Andre Pretelat, conducted a map exercise that closely resembled Fall Gelb's thrust. Pretelat's estimates of a German attack's speed were only off by a mere three hours. Gamelin accused Pretelat of pessimism and the exercise was kept secret.

It is also worth noting that some in the German high command shared the sentiments of Gamelin. Halder too thought the Meuse could only be reached in nine days at the earliest. Throughout Fall Gelb the German command was torn between two loose factions, the traditionalists and modernizers. The former feared that overextending panzers without proper infantry support would open up the German thrust to the dangers of an organized counterattack. The modernizers like Guderian favored a Bewegungskrieg (war of movement) and thought that mechanized forces and airpower would make up for the lack of infantry support. Lest we fall into the trap of at type of Calvinist historicism (modernizers are the elect and traditionalist the damned), remember that at various points Fall Gelb took extraordinary risks that could have been disastrous had the Allied forces acted more proactively. At the Battle of Sedan, the official Bundeswehr study of the campaign asserts that the local French commander had everything he needed to stop Guderian's thrust except an order to do so.

The German's key advantages were both concentration of forces and operational flexibility. Although the Allies had numerical superiority and a rough technical parity in the air (there's a lot of hair splitting in many of the comments as to how superior one force was over the other), the larger and arguably more important point is that German airpower had effected a numerical superiority over the schwerpunkt. This made it much harder for the French to suddenly shift their airpower over the Ardennes. The Luftwaffe enjoyed a relative proximity to the main bases and were not operating at a distance. German concentration was not limited just in airpower, the I Flak Corps was in full force and prevented Allied airpower from exploiting the gaps in the Luftwaffe air umbrella. Furthermore, the Flak arm proved instrumental in its dual use against French fortifications and Allied tanks (Rommel famously stopped the Cambrai counterattack with his mobile flak units). As Fall Gelb developed, German airpower lost these advantages in concentration of force and proximity to German airfields, and that is when losses started to creep upwards.

Overall, Fall Gelb was successful because it took a calculated risk that payed off handsomely. The Germans offensive played to their strengths, but they were aided considerably by the sluggard French high command. Fortifications in the Ardennes might have helped, or even stopped the German thrust, but that obscures the fact that the Ardennes thrust walked a knife's edge between success and catastrophe even without fortifications and facing reserve troops.

Sources

Citino, Robert Michael. Death of the Wehrmacht: The German Campaigns of 1942. Lawrence: University Press of Kansas, 2007.

Dildy, Doug, and Peter Dennis. Fall Gelb 1940 (1): Panzer Breakthrough in the West. Oxford: Osprey, 2014. 2014.

Epstein, Jonathan A. Belgium's Dilemma The Formation of the Belgian Defense Policy, 1932-1940. Leiden: Brill, 2014.

Frieser, Karl-Heinz, and John T. Greenwood. The Blitzkrieg legend: the 1940 campaign in the West. Annapolis, Md: Naval Institute Press, 2005.

Nord, Philip G. France 1940: Defending the Republic. New Haven: Yale University Press, 2015.

This topic was discussed in the Askhistorians podcast, episode 47, "The French Plan for WWII". Hope thats helpful, and sorry mods if this is against the rules.

Edit: To summarize what the podcast says(as the rules say I should do), France did not build fortifications along the Belgian border even after they determined war with Germany inevitable around 1937 for many reasons, the biggest being that fortifications there would basically be giving up Belgium, an ally, in the case of war. Politically, France could not have done this without risking their alliance with Belgium. This was not an acceptable risk for France because their war plans included Belgian assistance, and they did not want to give that up. Also, a large part of France's industry, including iron mines, were right on the Belgian border, and so building fortifications there would have disrupted industry and not even protected the mines (France knew that German artillery could have fired right over the fortifications and hit the industrial areas).

So, in short, France did play with the idea of building fortifications along their Belgian border, but political and practical issues kept them from pursuing it.