A lot of those "200,000 rifles" were Mle. 1916's, MAS-36's, and even 1886 Lebels. Most of these guns were incorporated into the German ToE and then assigned to guard/constabulary units, German Heer units on duty in France's interior, and were given to the second and third-rate units on and behind the Atlantic wall. The Germans also would walk into the factories they encountered in overrun territory and more or less order production of domestic designs to continue as normal, taking all production and shipping it to their depots.

Germany could never make enough K98's to arm everybody, and extensively used captured guns. A really good example is pistols. Redditor /u/R_Shackleford did a fairly comprehensive writeup a while back on all of the different pistols from other nations that Germany appropriated for use. They were pistol mad; instead of restricting their use to just ceremonial, officers, and flight crews...pretty much everybody had a damned pistol.

GREAT question! As /u/Caedus_Vao points out, I wrote a good bit about pistols over in some of the firearms forums. Generally they were re-issued as-is, mostly where-is, the large exception seems to be pistols.

For the most part, small arms, when captured, were distributed to the occupation forces in the general area as there are usually associated supplies that made widespread distribution a logistical challenge. There were no wholesale programs to refurbish or re-arsenal captured weapons and repairs were made in the field by field armorers when necessary.

New production from captured small arms factories was a little bit of a different story. Most places in Europe were producing variations of the Mauser rifle similar to what the Germans were issuing (eg: Poland, Czechoslovakia, Belgium, Hungary, etc) with the large outlier being France who was producing a different French design. The Germans would rather quickly convert Mauser production in occupied countries to the German pattern K98k standard (as in Czechoslovakia) or cease production altogether (as in Poland where parts and receivers were sent to Austria).

Pistol production, for the most part, was continued at full pace and distributed into the German supply chain. This worked somewhat OK as most of Europe at the time were producing handguns in common calibers (generally 7.65mm, 9mmk and 9mmp). Some efforts were made in the case of non-standard ammunition to distribute them to rear troops and occupation forces where production was somewhat local as we see in the case of the "French .32 Long" used in the Mle 1935. I wrote extensively on the topic in the post linked by /u/Caedus_Vao.

The Germans generally equipped second-line units (e.g. Volksgrenadier or police units) with this captured kit; and in many instances made their own conversions in order to simplify logistics or correct glaring errors in the original weapons systems.

The most important of the captured equipment was actually trucks, as the Germans never had enough and essentially made extensive use of every possible motor vehicle. The incompatibility of the spare parts for these trucks however resulted in a logistics nightmare - I believe the most extreme case had one Panzer Division needing spare parts for 100 different models of trucks.

Much of the captured kit moreover was from the Soviets, who lost enormous amounts of material to the Germans in the opening weeks of Barbarossa.

In particular the Germans made extensive use of captured Soviet sub-machineguns, and captured 76.2mm infantry/anti-tank guns were so plentiful that an entire line of assault guns in the Marder series were equipped with them. Funnily the Marder series itself is characterized by the use of many different captured tank chassis - from the French and Soviets mostly - since the Germans found many of these early war tanks to be inadequate due to the need for ever bigger guns for infantry support and anti-tank warfare. The only Allied tanks that seem to have been used extensively without much modification were the French Somua (which nonetheless had its cramped turret heavily modified), the Soviet T-34, and the American Sherman.