diff --git a/cpp/src/arrow/compute/kernels/codegen_internal.h b/cpp/src/arrow/compute/kernels/codegen_internal.h
index 405f35a9234b..d1b3f3528c2f 100644
--- a/cpp/src/arrow/compute/kernels/codegen_internal.h
+++ b/cpp/src/arrow/compute/kernels/codegen_internal.h
@@ -17,7 +17,6 @@
 
 #pragma once
 
-#include <concepts>
 #include <cstdint>
 #include <cstring>
 #include <memory>
@@ -1236,7 +1235,7 @@ struct GeneratorApplicator<Generator, Arg1, WithFirstTypeTwice, Args...> {
 
 template <auto Transform, auto TypeIdArray, size_t ArrayIndex,
           template <typename...> class Generator, typename... Args>
-  requires std::invocable<decltype(Transform), Type::type>
+  requires std::is_invocable_v<decltype(Transform), Type::type>
 auto GenerateKernelExecImpl(Type::type id) {
   constexpr auto kNumTypeIds = std::tuple_size_v<decltype(TypeIdArray)>;
   static_assert(ArrayIndex < kNumTypeIds);
@@ -1272,7 +1271,7 @@ auto GenerateKernelExecImpl(Type::type id) {
 
 template <auto Transform, auto TypeIdArray, template <typename...> class Generator,
           typename... Args>
-  requires std::invocable<decltype(Transform), Type::type>
+  requires std::is_invocable_v<decltype(Transform), Type::type>
 auto GenerateKernelExec(detail::GetTypeId get_id) {
   return detail::GenerateKernelExecImpl<Transform, TypeIdArray, /*ArrayIndex=*/0,
                                         Generator, Args...>(get_id.id);
diff --git a/cpp/src/parquet/column_reader.cc b/cpp/src/parquet/column_reader.cc
index 6aca8a23ce16..b9621ee32864 100644
--- a/cpp/src/parquet/column_reader.cc
+++ b/cpp/src/parquet/column_reader.cc
@@ -85,8 +85,9 @@ inline void CheckNumberDecoded(int64_t number_decoded, int64_t expected) {
 
 /// True if a T can hold a U.
 template <typename T, typename U>
-inline constexpr bool can_hold_v = std::in_range<T>(std::numeric_limits<U>::min()) &&
-                                   std::in_range<T>(std::numeric_limits<U>::max());
+inline constexpr bool can_hold_v =
+    std::numeric_limits<T>::digits >= std::numeric_limits<U>::digits &&
+    (std::numeric_limits<T>::is_signed || !std::numeric_limits<U>::is_signed);
 
 /// Clamp to a given type.
 template <typename T, typename U>