Yes, you can use your US passport for France.
When re-entering the UK, present your Egyptian passport and BRP. This also goes for the Eurostar-run UK exit checks if going to France by train (before French border control)
For entry to France, from Consulate General of France in Chicago:
American passport holders are not required to obtain a visa prior to visiting France -as tourists- for up to 90 days per semester (6 months).
For re-entry to UK, from GOV.UK:
You can use your BRP to confirm your:
Credit:stackoverflow.com‘
4 Mar, 2024
4 Mar, 2024
5 Mar, 2024