It's not like the French would really need to mobilize. Their standing army would have been adequate, as Hitler was well aware (hence his orders to break it off at the first sign of Anglo-French hostility). Of course, in all probability they didn't realize this and overestimated the Germans.
So from a purely-military standpoint, it would have been trivial for the Anglo-French to knock the Germans over in 1936 with the Rheinland as casus belli. But the economic and political (Lord Lothian summed up the British public's view nicely when he called it "no more than the Germans walking into their own backyard") realities of the time made it a non-starter.
The argument given was that the standing German army was more than enough to stop the standing French army, so to act at all the French would have to fully mobilize and reoccupy the Rheinland, as they didn't know about the orders on the German side to call of the reoccupation if there was French resistance. It would take time for the French to get into gear too, even with the standing army. Of course the Brits wanted nothing to do with it and were pressuring the French to do nothing. Things got really bad for France when in a panic over potential war, investors pulled their money out of the French banking system and sent it abroad, which rendered it insolvent and just sitting on a horde of untouchable gold due to the backing of their currency. Even paying for the standing army to move into the Rheinland would have probably been enough to cause a major financial crisis in France and probably would collapse the government. Remember that less than 2 years before there was a coup attempt in Paris by the Far Right, who hated the new Socialist government, so there were internal concerns too. France was not really prepared for war at all in 1936.
I wouldn't call the OTL build-up really gradual. The reality is that full-scale mobilization from scratch takes time and can't be done in a "quick" spending spree. Even with some prior covert measures, it took Germany around three years of reckless, economy-threatening spending to get their army to the point where they could legitimately smash a lower tier nation like Czechoslovakia or Poland and be in a position to wage a multi-year war against the Anglo-French (or even the Anglo-French-Soviets, although the main delay there would be down to how Stalin's purge had eviscerated the Red Army's officer corps). Not coincidentally, it also took that long for the Anglo-French to go from starting their full rearmament in the summer of '38 to being in the process of outstripping Germany when the Battle of France started in mid-1940. If anything, that means that their rearmament program was even more rapid then the Germans despite being more economically sound.
Exactly why it was gradual. The French couldn't spend too much for political and practical reasons. They got a late start and it cost them dearly. Also for Germany the big issue was rebuilding their demolished armaments industry, so their spending wasn't really even on the military per se as much as it was the industrial base behind it. For France they had to build up the necessary industry and try and do something about the fact that they had neglected not just R&D, but also personnel, equipment, and bases for their air force and army. Germany too had really been rearming covertly since the 1920s in terms of having shadow personnel, R&D, and even equipment stashed away. France in the meantime had cut their military budget to the bone and spent far too much on the Maginot line. And there was the fact that France was per capita just poorer and less industrialized than Germany, despite the higher standard of living in the 1920s-30s.
Also the outstripping of Germany in 1939-1940 was largely due to the reckless binge spending on US weapons, machine tools, and raw materials, which was even greater than what Germany had been able to afford during her rearmament period during the 1930s. They realized how badly they screwed up by taking a leisurely pace in the mid-late 1930s for their rearmament, so did it by busting their finances in 1939-40 (Britain was out of hard currency by the end of 1940). The Allies were buying so much from the US in 1939-40 US industry couldn't keep up and was buying back ammo and weapons from the US army to resell to the Allies with congressional approval.