Use gcc --target-help
-march=CPU[,+EXTENSION...]
generate code for CPU and EXTENSION, CPU is one of:
generic32, generic64, i386, i486, i586, i686,
pentium, pentiumpro, pentiumii, pentiumiii, pentium4,
prescott, nocona, core, core2, corei7, l1om, k1om,
iamcu, k6, k6_2, athlon, opteron, k8, amdfam10,
bdver1, bdver2, bdver3, bdver4, znver1, znver2,
btver1, btver2
...
It's often not the general architecture like x86 or x86-64 but the specific microarchitectures. But there's x86-64 (not x86_64) for a generic x86 CPU with 64-bit extensions. The full list for each architecture can be found on GCC's -march manual. For x86:
-march=cpu-type
Generate instructions for the machine type cpu-type. In contrast to -mtune=cpu-type, which merely tunes the generated code for the specified cpu-type, -march=cpu-type allows GCC to generate code that may not run at all on processors other than the one indicated. Specifying -march=cpu-type implies -mtune=cpu-type.
...
https://gcc.gnu.org/onlinedocs/gcc/x86-Options.html#index-march-13
While the baseline version of -march is -march=x86-64, the baseline / default tune option is -mtune=generic. That aims to not be terrible anywhere, avoiding performance pitfalls even at the cost of extra instructions or code size.
-march=native will pick the right arch and tune settings for the machine the compiler is running on, or tune=generic if the compiler doesn't recognize the specific model of CPU it's running on.
(e.g. old gcc on a Skylake, will still enable -mavx2 -mpopcnt -mbmi2 and so on, but will set -mtune=generic instead of something closer to appropriate.)