Jaeger Le-Coultre Watch with unique logo (is it real?)

We inherited this watch but are unsure of its origin. It appears to be legitimately very old, but I've not seen any other Jaeger Le-Coultre watches with the name displayed in this particular logo. It's very small and hard to read, but just says Jaeger Le-Coultre in a very small script font without the line underneath like in the logo now. Does anyone know anything about this watch? It has a six digit serial number on the back.