The Queensland-based company, which was founded in 1958 by Joe and Patricia Richardson, employs 500 people and generates annual revenue of about AU$130m (拢100m).
It specialises in the engineering, installation and maintenance of electricity networks, water utilities, telecommunications and industrial processes.
Vinci Energies was already active in Australia; as of the end of last year it employed 500 people there, generating about AU$140m revenue.
The purchase of J&P Richardson follows the recent acquisition of the HEB Construction and Electrix companies in New Zealand, in line with Vinci's strategy of expanding in countries with high economic growth rates.