Configure 1 ISP delivering two MPLS circuits into 1 layer 3 switch or router.

I don't see the MPLS links clearly identified on that diagram.   One can but guess.

It's also not clear if you want the MPLS "clients" to communicate with one another.

Assuming that the remote subnets are different than the main site's, then:
Insert a router in router / no NAT mode between the MPLS interface and the local subnet.
Set up a "link subnet" for the MPLS side of the router:
It might be 192.168.33.0/24 just as an example of one not likely being used.
Assuming the main site subnet is 10.0.10.0/24 and 192.168.1.0 is the remote subnet:
Main site gateway route 10.0.10.233 <> 192.168.33.1 to the MPLS
Main site MPLS router route 192.168.1.0/24 to 192.168.33.2 (the remote site end)
Remote site gateway 192.168.1.253 <> 192.168.33.2 to the MPLS
Remote site MPLS router route 10.0.10.0/24 to 192.168.33.1 (the main site end)
THEN, you add a route in the main site gateway router: 192.168.1.0/24 to 10.0.10.233
AND, you add a route in the remote site gateway router: 10.0.10.0/24 to 192.168.1.253

With this, the outgoing packets will hit the gateway, be redirected back to the MPLS router and on to the other side where the packets will come out of the router, bypassing the gateway at the destination.  And, packets hitting the MPLS router will be directed to the mating MPLS router at the other end.
Return packets will hit the local gateway, be redirected back to the MPLS router, be directed to the mating MPLS router on the other end,  and on to the other side where the  packets will again come out of the router, bypassing the gateway at the destination.

If the gateway routers are capable enough, they may block the return packets because there is no sequence or "state".
In that case, there needs to be a setting that will turn this off or ameliorate the difficulty it causes.  e.g. an ALLOW kind of rule.  i.e. ALLOW 192.168.1.0/24 and ALLOW 10.0.10.0/24 at the other end.  I'm not very clear about this because routers do vary.

Hi Fred,
sorry I didn't give full detail. What I want is both circuits to communicate via BGP protocol in which that's how I will need to communicate to my ISP.
My diagram shows two links from 1 ISP which they are doing the load balancing on their end, and my job is to have those two links terminated on L3 switch or a router with bgp protocol in place and configure.

Hope that explains my scenario that I like to configure on my L3 switch or router.

So where is the MPLS?
I must admit that I have not much experience with this sort of thing.
My experience with MPLS is with private links.

I see that:  MPLS can encapsulate packets of various network protocols, hence its name "multiprotocol".
So I'm wondering how this fits with the BGP.
I wonder how the MPLS small path labels work with BGP in general?
No answers I'm afraid .....