I don't have formal theological training.
The idea of "common grace" has been intuitively acceptable to me for a long time. My understanding of it has been that God's grace in the lives of believers affects others- their families, workplaces, communities, even nations. For the sake of those He has chosen to redeem, His work in their lives has a positive effect wherever they go. He even restrains evil and brings about good for their sakes.
Did Mr Calvin believe in this? It sure seems so. What God did through his obedience and faith to apply scripture to all of life helped clean up Geneva and make it a hospitable place for refugees and a place where all-of-scripture could be applied to all of life- and even exported.
Without being too technical, it also seems that since the elect includes those who God has chosen but have not yet come to faith (e.g. someone who will become a Christian at the appointed time of regeneration), God's grace is also present there and in that person's surroundings.
As I read Scripture, this is really easy to understand and believe. It's not in any way to say every person gets mercy rather than justice, or that things will always seem good or fair, but what God does is, by definition, good. Everybody, in some way, benefits from God's gracious goodness.