Phanerozoic CO2 atmospheric levels:
Biosphere has been consuming CO2 and storing it in the lithosphere since the Cambrian explosion.
The cyclic pattern is related with the tectonic cycles, named the Wilson Cycle, wich has formed two super continents during Phanerozoic period: Rodinia and Pangea.
When a super continent breaks, a new ocean is formed and after Cambrian CO2 begins to get stored in the carbonate platforms close to newly formed coastlines, reducing the levels in the atmosphere.
When the ocean formed in a Wilson Cycle is old enough, oceanic crust begins to subduct the continents and after Cambrian part of this carbon returns to the atmosphere from calc-alkaline magmas of volcanic arcs. This is what is starting to happen in the Atlantic Ocean.
Currently, the Atlantic has three isolated subduction zones: the
Lesser Antilles in the Caribbean, the Scotia Arc in the South
Atlantic, and the Gibraltar Arc in the Mediterranean.
Part of the CO2 gets stored in the Continental Crust, staying in the lithosphere reservoir in the form of CaCO3. So the balance of Wilson Cycle since the Cambrian is a reduction of CO2 in the atmosphere (shown in the first graph), and an increase of Continental Crust. The second consequence applies for the hole Earth History where the Wilson Cycle has been operating.
A teacher told us in University the Pacific ring is more powerfull than Atlantic dorsal, and Atlantic Ocean is going to disappear. If that is true, in the following millions of years, part of the CO2 stored in the Atlantic Ocean will return to the atmosphere.
So answering your question, the Earth would not run out of CO2 in the next million years with no human intervention. Some CO2 stored in the Atlantic Ocean is going to be released to the atmosphere. Maybe in the next Wilson Cycle when the Atlantic Ocean closes forming a new supercontinent and breaking again forming a new ocean, but it is a nosense to talk about climate in said 100my as human technology for sure will modelate climate in the future.
Apart from volcanism are there any processes that return carbon captured in fossil fuels and limestone to the atmosphere?
Apart from humans burning fossil fuels and volcanism, CaCO3 starts to dissolve in the oceans at certain profundity/pressure. The level when CaCO3 start to dissolve is known as Carbonate compensation depth (CCD). The ocean is in equillibrium with the atmosphere because of Henry's law so that affects atmospheric CO2 levels.