You can't store as fast as on local HDD, What's your LAN bandwidth? I assume today's 1 Gbps standard.
And how many users share it and what other LAN traffic goes through there?
And how fast are the file share HDD? Do you use SSD?
That's what you can do on the hardware side. Use fast drives and network hardware.
On the software side, you can index your data ideally for your queries, that's "a science in itself", but no index accelerates writes! Every index needs to be written and updated when you insert or update data. There's no reason to avoid indexes because of that because read operations are much more frequent and so writing the indexes is a benefit for the whole speed. The fasters users read, the faster bandwidth also is available for the write operations.
But you can't force your data up the wire into the DBF faster than the combination of network speed and HDD speed allow on top of needing the CPU resource of the file server to care for your write operation, too. The limiting factor most often is the LAN, you would need very strange situations of concurrent updates of very many tables sitting in far apart HDD sectors of a traditional platter drive so writing is slowed down, but even in these drives write operations will then be queued and handled better than just in the chronological order they come in.
If you want shared data you have no choice other than LAN.
What write times are you experiencing in what hardware environment? The question is whether you really just have bad hardware or illusionary expectations despite having a modern network backbone and file server.
Using another backend, MSSQL Server means another balance of resource needs. Data still has to travel the network, that aspect doesn't get improved by SQL Server. In write operations a client is done when sending over the SQL Insert/Update statements, the time the server needs to write this out are not the clients concern anymore, but that service needs more CPU resources on the server side, more RAM to cope with databases caching and transactions and more HDD for having transaction logs VFP DBFs don't write. This can get faster but doesn't necessarily become faster.
What you'll never get is the write speeds of local writes, but that doesn't allow sharing the data, does it? If you make one client the file server, only that client will have the advantage of writing faster. And you pay that with a high price as clients are not good at being file servers.
If you're using a NAS device attached to some router in your network, double check the effective bandwidth isn't down at rates of poor WLAN because clients don't use cable connections or the NAS itself only is attached with 100Mbit, that all should be at the normal technology levels of today.
Bye, Olaf
Olaf Doschke Software Engineering